text: Numerade Educator 00:38. Find the probability of each event. 021 You will be able to calculate the mean and standard deviation of a discrete random variable. The probability of selecting a sophomore is 12/26 (right!), and the probability of selecting a female is 15/26 (right!). Thus, the probability that a randomly selected. b) Find the probability of rolling a sum of no greater than 5. ate breakfast, if the student was a female 6. Giving a test to a group of students, the grades and gender are summarized below A B C Total Male 7 20 14 41 Female 3 4 19 26 Total 10 24 33 67 If one student is chosen at random, Find the probability that the student was male OR got an A. What is the probability that the sample mean FNE score is between 18 and 18. If one student is chosen at random from year 7, find the probability that this student does (a) both art and music (b) only art (c) only music solution: 47+59=106 But there are only 100 students!. Independence and Conditional Probability. Students are selected randomly. " (a)Find the probabilities of the events below. a) Find the probability that his/her grade is greater than 80. What's probability that both will be girls?' and find homework help for other Math. Of the physics majors, 3 are female. At Hillgrove, 60% of the students carry a backpack or a wallet. It contains 12 hats, 15 noisemakers, ten finger traps. etc) Combining Normal Random Variables Example. Question: A class consists of 68 female students and 80 male students. Out of a group of 10 statistics students, 3 are randomly chosen to win prizes: the 1st person chosen gets a dog, the 2nd person chosen gets a hamster, and the 3rd person chosen has to pay money to avoid getting a cat. What is the probability that a randomly chosen college football team had a losing record in 1998? 3. In a management trainee program, 80% of the trainees are female, while 20% are male. c) What is the value of P (M U S)? , 1 d) Complete this sentence using and or or: P (M U S) is the probability that a randomly selected car has a manual transmission e) What is the value of P (SC)? Explain the meaning ofP(SC). The chance that someone chosen at random is female is about 1/2. four adults from a particular town. In addition, the probability that randomly selected student has at least one household member who smokes and. Ex 10) In a recent study it was found that the probability that a randomly selected student is a girl is. 9 (c) or or 0. In this scenario, the marginal probability is not the same as the conditional probability. (b)Select the probability that is equal to. the Of 14) At o ZOO footbal. If a student is selected at random from this senior class, what is the probability that the student is: a) female and owns a car? b) male and does not own a car?. What is the probability that a randomly selected person was born on New Year's Day (ignore leap year)? Question: what is the probability that the student was a woman? 9. In a math class there are 8 male students and 7 female students. Random Variables and Probability Distributions 169 p(z>2. randomly and independently. What is the probability that a student is female and going to college? IOC). A recent survey suggests that 85% of college students have posted a profile on Facebook, 54% use nd 42% do both (b) Suppose we select a college student at random and learn that the student has a Facebook. If a tennis player was selected at random from the group, find the probability that the player is (a) male and left handed;. a) Find the probability of rolling a sum of at least 9. What's probability that both will be girls?' and find homework help for other Math. Of all the female students, the probability that a student has short hair. P ( F | G) = 2213 5000. The chance that someone chosen at random is female is about 1/2. complete parts (a) and (b) below. Out of the individuals over age 64, find the probability that a randomly selected individual was a black or white male. 4 (together the probability is 1) Now, if you get Sam, there is 0. Example 9: You pack a cooler for the beach and stock it with soda cans. An urn contains six red balls and eight green balls. If 1 animal is selected at random, what is the probability of selecting a. It is commonly denoted by a symbol such as x. Snow's homeroom, what is the probability that the student is taking Algebra Il and Chemistry? Explain your reasoning. 1 - = Answer: 4. You have just become a parent of twins and. What is the probability that a person selected at random from the survey group is male? Explain your reasoning. a) Find the probability that his/her grade is greater than 80. The events of interest are “female” and “right-handed. Offered Price: $15. It deals the analysis of the frequency of past events. Find the probability of drawing the given card. Find the probability that a randomly selected individual was a black female. 9898 Solution 4-25 n. statistics. What is probability the committee has exactly 3 boys? Question 3 [10 marks]. 👍 Correct answer to the question A florist used 14 flowers to make a bouquet including 6 daisies what is the probability that a randomly selected flower will be a daisy - e-eduanswers. Based on the data, answer the following question: 2. A red king 20. A pair of dice are tossed. Find the probability of rolling a 2 or an odd number. Find the probability that a randomly selected student is. A couple plans to have four. What is the probability that a randomly selected female. What is the probability that a book selected at random is a paperback, given that it is non-illustrated? ra. is a female student. 37) The academic register compiled data on 11 000 students which were summarized in a contingency table. Your science teacher will choose 5 students at random to create a group to do a project. Question # 00189286 Subject Business Topic General Business Tutorials: 1. What is the probability that a student chosen is female? b. A survey of an introductory statistics class in Autumn 2003 asked students whether or not they ate breakfast the morning of the survey. This makes probability samples more representative, and. A UPS package is randomly selected and X is the weight in pounds of the package. 11 years 13 years 15 years Female Male a. check_circle Expert Answer. four adults from a particular town. The resulting data are summarized in the table below. When calculating this probability, we are given that the student is full time. (b)Select the probability that is equal to. There are 38 + 30 + 51 + 10 + 4 + 8 + 137 + 67, or 345 students in the senior class. heights of university students. Det är gratis att anmäla sig och lägga bud på jobb. Find the probability that a randomly selected individual was black; Find the probability that a randomly selected individual was a black or white male. It is a vowel. Which problem requires the. Out of the individuals over age 64, find the probability that a randomly selected individual was a black or white male. A randomly selected student prefers a meat topping. A student is selected at random. 57 24 to 29 0. If a salesperson comes to a particular school promoting a book, what is the probability that this person is female? 6. b What is the probability that a randomly selected student: is male and does not play the violin ii plays the violin?. A survey asked students which types of music they listen to? Out of 200 students, 75 indicated pop music and 45 indicated country music with 22 of these students indicating they listened to both. Among male birds of a species, 20% have a particular gene. Find the probablility that the person chosen at random. Basic Probability. It is from the upper half of the alphabet. What is probability the committee has exactly 3 boys? Question 3 [10 marks]. [4] (a) or 6% or 0. in a class 10 boys and 5 girls. The resulting data are summarized in the table below. Use these results to estimate the probability that: a. 9973 for two people and you have about 0. b) If a student is selected randomly, calculate the probability that they are male and in grade 9 or 10. What is the sample space for this probability experiment? b. The probability that a randomly selected student is in the marching band and not an engineering major 120 O. Find the probability that a randomly selected individual was black; Find the probability that a randomly selected individual was a black or white male. 120 are male, 50 are upper division students, and 40 are upper division male students. Statistics- What is the probability that a randomly selected manager is 35-44 years old. There are 137 + 4 + 8 + 10, or 159 students who participate in athletics. You and a randomly selected student from your class both earn A's in this course. 021 You will be able to calculate the mean and standard deviation of a discrete random variable. A class of 40 students has 11 honor students and 10 athletes. - candidates were told that the positions were randomly filled. 5% of Texans do not have health insurance as of June 2012. A student is randomly selected and X is the number of correct answers on a two question multiple-choice quiz. What is the probability that the number chosen is not odd? 0. 363 while 57% of the workers at City Bank are female. Example 5: Assign a probability to each following event based on the information provided. Grade Males Females 9. P(female) C. 2) If a student is selected at random from Ms. A family that is known to have two children is selected at random from amongst all families with two children. Fifty (50) senior athletic students attending major universities are randomly selected and recorded in order of selection. Probability and Probability Distributions Problems Q. Find the probablility that the person chosen at random. 435 P(allergies) = 18/40 = 0. The KW test examines respondents’ knowledge about the duties in their workplaces and the knowledge about the Australian and Tasmanian labour markets. The height of students at Palomar. In this scenario, the marginal probability is not the same as the conditional probability. What is the probability of a randomly selected student passing Mrs. Find the probability that a randomly selected individual was a black female. What are the odds that Student A will be selected to clean the board today? The probability of Student A being selected is$1/10$. In non-probability sampling, each member of the population is selected without the use of probability. assistants, and 8 female teaching assistants. A simple random sample or SRS consists of n elements from the population chosen in such a way that every set of n individuals has an equal change of being the sample actually selected. Randomly selecting a person with type A blood Randomly selecting a person with type O blood c. The probability that a randomly selected student from a college is a female is. Find the probability of a student taking Chemistry, given that the student is not taking Algebra II. Ruby's dog has 8 puppies. If there is also 60% that do not play soccer, calculate the probability that a student chosen at random from the class: 1 Plays soccer only. A card other than a 2 Find the probability of winning the lottery according to the given rules. Round to the nearest thousandth as needed. In a class of 50 students, 32 are Democrats, 16 are business majors, and 6 of the business majors are Democrats. Example 3 Suppose that the height of UCLAfemale students has normal distribution with mean 62 inches and standard deviation 8 inches. probability that both events A and Boccur. 36 animals are in a zoo: 6 male and 12 female monkeys, 6 male and 10 female chimpanzees, and 1 male and 1 female lion. Given that a randomly selected student is a sophomore, what is the probability that he/she is left-handed? What we know:. A couple plans to have four. The heights (in inches) are as follows: 67, 59, 64, 69, 65, 65, 66, 64, 62, 64, 62. is female and ate breakfast 4. Use the table below to find each probability for a randomly selected employee: EDUCATION AND SALARY OF EMPLOYEES Over$30,000 14 245 Use the table to find each probability for a randomly chosen student. A survey asked students which types of music they listen to? Out of 200 students, 75 indicated pop music and 45 indicated country music with 22 of these students indicating they listened to both. What is the probability that if a stu entwa female that they got a passing gr e. Example: The distribution of 1237 college students by sex and major is given below. 8% have both defects. Based on the data, answer the following question: 2. What is the probability that a student is female and going to college? IOC). Find the probability the student is male, given that they prefer pepperoni. 3 Conditional Probability, Intersection, and Independence Example 2 If 60% of a department store's customers are female and 75% of the female customers have credit cards at the store, what is the probability that a customer selected at random is a female and has a store credit card? 5. if the first person selected of the 10 is female the probability the next person is female would not change) then we can treat this information like it comes from a binomial distribution, where random variable X = number of female selected out of 10 trials. Find the conditional probability of intent to graduate, given that the student is a male. Thus, the probability that a randomly selected. For all the melons at the grocery store, 70 percent of the melons are provided by Distributor J and 30 percent are provided by Distributor K. Find the probability That a randomly chosen student is a male and intends to graduate. Left handed Right handed Total Male 3 29 32 Female 2 16 18 Total 5 45 50. Estimate the mean height of all female students at this college. 12 ID Age Group (yr): Probabilit 18 to 23 0. 4 (together the probability is 1) Now, if you get Sam, there is 0. In a major Midwestern university, 55% of all undergraduates are female, and 25% of all students belong to a Greek organization (fraternity or sorority). Ruby wants to keep one puppy. Find the conditional probability of different majors among the female students of CMSU. What is the probability that he drinks 2 or 3 cups in a day? 4. If two are selected at random without replacement, find the probability that both are defective. What is the probability she rates the library services as good? f) A randomly selected person who completed the survey rated the library services as good. If a student is randomly selected, what is the probability that the student is a senior or a female?. Question # 00189286 Subject Business Topic General Business Tutorials: 1. (a) What is the probability the student visited the tutoring center four or more times, given that the student is full time? Conditional probability is all about focusing on the information you know. If a student is selected at random, find the probability of selecting (a) a junior or a female (b) not a junior male. ate breakfast, if the student was a female 6. Find the conditional probability of intent to graduate, given that the student is a male. is a female student. An examination consisting of ten true-or-false questions was taken by a class of 100 students. Probability 8. However, Student Records did provide us with the appropriate quotas for male and female students, which showed a 53:47 male-female ration [note: this is a fictitious figure]. A female is selected, then a male. A randomly selected student prefers a meat topping. Use a Venn diagram to find the probability that a randomly selected student listens to pop music given that they listen country music. Education Male Female. Major This Major Female Male Business 20 36 64 Humanities 9 65 35 Education 10 65 35 Social science 10 52 48 Natural sciences 8 57 43 Other 43 47 53 (a) What is the probability that a student selected at random from the freshman class is a female? (b) What is the probability that a business student selected at random from the freshman class is. What is the probability that a randomly chosen college football team had a losing record in 1998? 3. Find the probability that a randomly selected observation exceeds26. d) Find the probability of rolling a 3 or a 4 on the green die. What is the probability that out of 6 randomly selected students exactly 4 are female? d. If a student is selected at random, find the conditional probability that (a) the student is female given that the student is majoring in computer science; (b) this student is majoring in computer science given that the student is female. If we assume that the probability of a female or male being selected is constant (i. Get an answer for 'A class has 11 boys, 9 girls. What is the probability of a randomly el. Its says that a randomly chosen student is a female and does not have a laptop. An athlete is randomly selected. In this situation there are n = 125 identical and independent trials of a common procedure, selecting a student at random; there are exactly two possible outcomes for each trial, “success” (what we are counting, that the student be female) and “failure;” and finally the probability of success on any one trial is the same number p = 0. What is the probability that the number chosen is not odd? 0. He pitches 50% of the games. Sports Teams. What is the probability that a randomly selecte 39 s given hat student is a freshman. In a litter of 8 kittens, there are 2 rown emales, I ro ale, 3 spotted females, and 2 spotted males. 1 - = = Answer: 3: A number from 1 to 5 is chosen at random. athletics program is equal to the probability that a randomly selected student who is female participates in an after-school athletics program. We must subtract these students before calculating the relative frequency: [latex]P(\mathrm{Health\; Science\; or\; female. What is the probability of a randomly selected student is male? 8. Choose a student from the class at random. 3 Plays only one of the sports. P(female brown). randomly selected student at this high school they had al least one family member living in house who smoked. What is the probability that a randomly selected DWI suspect is given…. business degrees nonbusiness degrees total male 189131 634650 823781 female 169539 885329 1054868 total 358670 1519979 1878649 (a) find the probability that a randomly selected student is male , given that. What is the probability that a randomly chosen student likes history the most? UI/2Llo 13. Find the conditional probability of intent to graduate, given that the student is a female. Use the table below to find each probability for a randomly selected employee: EDUCATION AND SALARY OF EMPLOYEES Over $30,000 14 245 Use the table to find each probability for a randomly chosen student. 12 {/eq} (a) The probability that a randomly selected civil engineering major is a female. A second student is randomly selected to go to the office. A single die is rolled. What is the probability that a boy is chosen as a %. If a student is selected at random from Ms. Check out a sample Q&A here. You must correctly select 6 out of 48 numbers. P(B/A)= Probability of female+ does not own laptop. Want to see the step-by-step answer? See Answer. Define random variable. A random sample is defined as a sample where each individual member of the population has a known, non-zero chance of being selected as part of the sample. The student body of a large university consists of 60% female students. Find the probability that both are men. The student has a B average and does NOT play football. What is the probability that a person selected at random from the survey group is male? Explain your reasoning. find the probability that. What is the probability that a student chosen is female? b. If we know that a randomly selected student has a pierced ear, what is the probability that the student is male? Gender What is Conditional Probability? occurrllÐ alread,J Gtv6Ñ Calculating Conditional Probabilities Co-cawJb- +r;aÿ. Left-handed Right-handed Male 2 35 Female 6 36 a. The grades of a group of 1000 students in an exam are normally distributed with a mean of 70 and a standard deviation of 10. Of the males, 40% of them belong to a Greek organization. The chance that someone chosen at random is female is about 1/2. Suppose that 40% of mathematicians are female. What is the probability that a person selected at random from the survey group is female? Explain your reasoning. A card other than a 2 Find the probability of winning the lottery according to the given rules. + Round all final answers to 4 decimals. A student from this group is selected randomly. 06 means in this setting. What is the probability that a randomly selected student owns a home, given the student is a female? fullscreen. the c selected foot t that o selected plays 15) A to status here Stock C!çrks 12, + S employee. Find the probability that a randomly selected individual was black; Find the probability that a randomly selected individual was a black or white male. students are selected at random from this group. Estimate the mean height of all female students at this college. Student Loss in Pounds 1 2. (b) If a sample of 35 students are selected randomly, find the probability that the sample mean is above 500. A UPS package is randomly selected and X is the weight in pounds of the package. find the probability that. the c selected foot t that o selected plays 15) A to status here Stock C!çrks 12, + S employee. The studenthasasister. 1 - = = Answer: 3: A number from 1 to 5 is chosen at random. What is the probability that at least two students share a common birthday month? (10) Nine balls are randomly withdrawn from an urn that contains 10 blue, 12 red, and 15 green balls. A math class consists of 25 students, 14 female and 11 male. A math class consists of 14 female students and 16 male students. Sports Teams. Event A: Lila selects a green ribbon. What is the probability that a randomly selected female. A random variable is a function defined on a sample space. What is the probability that a randomly selected male plays neither sport? So, 11) Selecting a Student In a statistics class there are 18 juniors and 10 seniors; 6 of the seniors are females, and 12 of the juniors are males. A random sample of 140 students is selected and asked if they get their lunch from the salad bar in the cafeteria. What is the probability that an “A” student is male? 5. (a) What is the probability that a randomly selected student has completed the assignment? I q Il 30 17 (b) Are the events "selecting a female" and "selecting a student who completed the assignment" independent? Justify your answer. 12 {/eq} (a) The probability that a randomly selected civil engineering major is a female. In non-probability sampling, each member of the population is selected without the use of probability. The probability of rolling a 5 is P(A)=1/6 Example: roll a die This isEvent E: getting an even number. (a) Find the probability that a randomly selected student is a male binge drinker, and find the probability that a randomly selected student is a female binge drinker. ' and find homework help for other Math questions at eNotes. What is the probability that a randomly selected DWI suspect is given…. 23% student will be female in CMSU if randomly selected 2. Conditional probability Given that a under-graduate student is selected at random, what is the probability that this student is a nurse? Restricting our attention on the column representing undergrads, we find that of the 90 undergrad students, 53 are nursing majors. If 1 animal is selected at random, what is the probability of selecting a. What is the probability that a randomly selected student got a A or B? ao + 15 coo too 4. If a student is selected at random, find the probability of selecting the following. getting a female getting a male or a junior -zUD getting a junior or a senior 2,140 getting a female sophomore 2¥0 getting a female, given that the student is a junior getting a sophomore, given that the student is male. 1 - = Answer: 4. A single die is rolled. The 66% (660/1000) chance of a humanities major being female is a a. Offered Price:$ 15. the probability of the student being female is 0. Multiply that by the 0. What is the probability that a randomly selected student is female? b. 60 12) The random variable X is the number of siblings of a student selected at random from a particular secondary school. Compute the probability that a male is selected, then a female. 4: Conditional Probability Name: _____ www. A committee of six is randomly selected from a club with 18 male and 12 female members. (a) Explain what probability 0. Of the female students , 25% live off campus. Find the height above which is the tallest 5% of the female students. Find the probability that a randomly selected individual was black; Find the probability that a randomly selected individual was a black or white male. If a student is selected at random, find the probability of selecting the following: a) P(a junior or a female) b) P(a senior or a female) c) P(a junior or a senior) 14) At a particular school with 200 male students, 58 play football, 40 play basketball and 8 play both. None of the above. A random sample of students is selected, and each one is asked to search for a certain subject using Google and then MSN, or vice versa. heights of university students. Sex Arts and Sciences Business Music Total Male 127 383 40 550 Female 380 242 65 687 Total 507 625 105 1237 Find (a) the probability a randomly selected student is Music major; (b) given that the randomly selected student is Music major, what is the probability that. (b) Find the probability that a randomly selected three-year-old female weighs between 25 and 35 pounds. Rounding Calculato. Find the probability that a student plays a competitive sport, given that the student is female. d) Find the probability of rolling a 3 or a 4 on the green die. Find the height below which is the shortest 30% of the female students. At Hillgrove, 60% of the students carry a backpack or a wallet. Example Of the students at a certain college, 50% regularly attend the football games, 30% are rst-year students and 40% are upper-class students (i. If a conditional probability, also state which variable is given. P (being male or a being a nursing major) (Round to the nearest thousandth as needed). What is the probability of randomly selecting a card from a standard 52 card deck and having the card be a face card or an odd numbered card?. statistics. What is the probability that a randomly selected student is enrolled in a mathematics B. About 25 percent of the students are female but not C students. STATISTICS AND PROBABILITY CHAPTER 4. A red king 20. 9 (c) or or 0. A student from this group is selected randomly. 5 inches and a standard deviation of 4 inches and the height F of female speed daters follows a Normal distribution with a mean of 64 inches. If a random sample of twenty students is selected, a. b) If a student is selected randomly, calculate the probability that they are male and in grade 9 or 10. Find the conditional probability of intent to graduate, given that the student is a male. Round your answer to three decimal places if necessary. In a sample of 1000 students majoring in the humanities, 660 were female. Major This Major Female Male Business 20 36 64 Humanities 9 65 35 Education 10 65 35 Social science 10 52 48 Natural sciences 8 57 43 Other 43 47 53 (a) What is the probability that a student selected at random from the freshman class is a female? (b) What is the probability that a business student selected at random from the freshman class is. A random variable is a function defined on a sample space. Find the conditional probability that a student selected at random is a computer science major given that he/she is a senior. Out of a group of 10 statistics students, 3 are randomly chosen to win prizes: the 1st person chosen gets a dog, the 2nd person chosen gets a hamster, and the 3rd person chosen has to pay money to avoid getting a cat. We also know that 8% of the yoga students study with Patrick and are female, while 66% of the students study with Carl and are female. In a class of 50 students, 32 are Democrats, 16 are business majors, and 6 of the business majors are Democrats. 20% of the females and 30% of the males play the violin. , people, houses, phone numbers, etc. If a student IS selected at random, what is the probability that the student will be a [email protected] hair? 20. The probability distribution of the random variable X,whereX denotes the number of questions answered correctly by a randomly chosen student, is represented by the accompanying histogram. 255 x 2 (d) (1 - 0. El Dorado Community College considers a student to be full-time if he or she is taking between 12 and 18 units. Find the probability of drawing the given card. The air pressure in an automobile tire. x P(X = x) 0 0. 9 (c) or or 0. Find the probability that a randomly selected student is female or a physics maj. Round to the nearest thousandth as needed. According to the U. (c) If P(X < k) = 0. It is commonly denoted by a symbol such as x. The following chart shows favorite subjects of students based on their gender. Additional Exercises for Section 5. d) A randomly selected person who completed the survey is male. Eight-five percent of TCW students take math and 72% take science. If a student is randomly chosen, what is the probability that the student participates in only drama and band? 62/87,21 a. Check out a sample Q&A here. If a student is chosen at random, what is the probability that the student is a male in Grade 11? 22. What is the probability that a randomly selected student is a female who ate breakfast? P(F and B)= 125/332 or 0. three students are selected random one after the other. If a randomly selected student is a female student, what is the probability that she is a C student? Content header: Conditional. If a student is selected at random from this senior class, what is the probability that the student is: a) female and owns a car? b) male and does not own a car?. Find the probability of drawing the given card. The king of diamonds 5. If 1 animal is selected at random, what is the probability of selecting a. What are the odds that Student A will be selected to clean the board today? The probability of Student A being selected is $1/10$. 1)first two are boys and third is girl 2)first and third is of same gender and third is of opposite gender. Question: Of all the yoga students in a particular area, 20% study with Patrick and 80% study with Carl. Question: What is the probability that a randomly selected student is either a Health Science major or a female? Answer: There are 644 Health Science majors and 6,198 females, but 421 students are counted twice because they are both Health Science majors and female. 58, while the probability of that student being an out of state resident is 0. 6 of the female students are enrolled in the Accounting class, 4 in the Economics class and 5 in the Statistics class. The student body of a large university consists of 60% female students. - candidates were told that the positions were randomly filled. All 63) ---. Left handed Right handed Total Male 3 29 32 Female 2 16 18 Total 5 45 50. Are eating breakfast and gender independent?. What is the probability that a randomly selected student has a scaled test score of at least 90? (Ga. Find the probability of drawing the given card. defective part fails within the ﬁrst year with probability 0. By completing this table or otherwise, find the probability that a) a student selected at random prefers to watch television; 38 100 b) a student prefers to watch television, ven hat the student is a boy. Explain how you Qund your answers. RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS: STUDENT OBJECTIVES FOR THE AP EXAM 0. What is the probability that a person selected at random from the survey group is male? Explain your reasoning. three students are selected random one after the other. There is a 40% chance of rain during the game tomorrow. A letter is selected at random from those in the word TRIANGLE. check_circle Expert Answer. A Detailed Explanation. A survey of an introductory statistics class in Autumn 2003 asked students whether or not they ate breakfast the morning of the survey. the probability of the student being female is 0 In a school, the probability that a student takes environmental science and geography is. Find the conditional probability of different majors among the female students of CMSU. In a group of 294 students, 130 are seniors and 121 are males. 2 Plays basketball only. This table records the data. If a student IS selected at random, what is the probability that the student will be a [email protected] hair? 20. P(F|C) = ? Use the formula swapping F and C from the previous example: P(F|C) = P(F&C)/P(C) We have P(C) =. Of all the female students, the probability that a student has short hair. Find the probability that a randomly selected student om your Class has either a sister or a brother. Of the students in the sample, what percentage is younger than 20 years of age? If a customer is female, what is the probability that she is single? What percentage of customers is male? What is the probability that a randomly selected bill will be at least $39. On a television game show, 9 members of the studio audience are randomly selected to be eligible contestants a. Female 30 50 a. Giving a test to a group of students, the grades and gender are summarized below A B C Total Male 7 20 14 41 Female 3 4 19 26 Total 10 24 33 67 If one student is chosen at random, Find the probability that the student was male OR got an A. After calculation we got the result that probability of 53. Find the probability that a randomly selected individual was black; Find the probability that a randomly selected individual was a black or white male. Its probability distribution is given in the table. The 66% (660/1000) chance of a humanities major being female is a a. In a class of 50 students, 32 are Democrats, 16 are business majors, and 6 of the business majors are Democrats. What is the probability that a randomly selected yoga student is female, given that the person studies yoga with Carl?. Estimate the mean height of all female students at this college. is [email protected] breakfast 5. Find the probability that (a) five red and two green balls are selected. b) Find the probability that his/her grade is less than 50. This is the currently selected item. complete parts (a) and (b) below. A final exam in Math 160 has a mean of 73 with standard deviation 7. Question: Of all the yoga students in a particular area, 20% study with Patrick and 80% study with Carl. 20% of the females and 30% of the males play the violin. What is the probability of the outcomes summing to five?. Find the probability that a randomly chosen student received an A in general chemistry o calculus or both. Estimate the mean height of all female students at this college. Education Male Female. A class consists of 45 students. A student randomly chooses 3 of the courses to enroll in. Female 125 74 199 Total 140 331 191 Find the probabilitvt at a randomly selected student Iqq 331 l. What is the probability that a randomly selected student is female, given that the student ate r. In a bag of marbles there are 5 green, 6 red, and 4 yellow. This is the currently selected item. In a survey, 3 of 4 students said the courts show "too much concern" for criminals. The two-way table summarizes the class data. Use appropriate notation and round to four decimal places. Probability Sampling. If 24 students are randomly selected, find the probability that the mean of their test scores is less than 76. What is the probability that there is a conflict in the student's schedule? iii) A committee of 5 students is selected a random from a group consisting of 10 boys and 5 girls. 0% have either a faulty switch or a defective cord, 2. The accompanying table shows the numbers of male and female students in a particular country who received bachelor's degrees in business in a recent year. ate breakfast, if the student was a female 6. _____ There are 4 green marbles and 3 white marbles in a bag. What is the probability that among the students in the sample exactly two are female?. 40 play 8 play both. Find the probability that a randomly selected student is. The table gives the number of degrees earned in a certain university in the 2007-2008 academic year. There is a 40% chance of rain during the game tomorrow. 06 (b) or or 90% or 0. The discrete random variable X that counts the number of successes in n identical, independent trials of a procedure that always results in either of two outcomes, "success" or "failure," and in which the probability of success on each trial is the same number p, is called the binomial random variable with parameters n and p. athletics program is equal to the probability that a randomly selected student who is female participates in an after-school athletics program. What is the probability that a randomly selected female student majors in civil engineering? Round your answer to two decimal places. What is the probability a randomly selected bird of this species has the gene? p. b What is the probability that a randomly selected student: is male and does not play the violin ii plays the violin?. University of North Carolina, Greensboro ECO 25 Chapter 5 DISCRETE PROBABILITY DISTRIBUTION. Thus, the probability that a randomly selected. The probability of a "success" remains the same from one trial to the next, and this probability is denoted by p.$25,000 - \$34,999. What is the probability that at least two students share a common birthday month? (10) Nine balls are randomly withdrawn from an urn that contains 10 blue, 12 red, and 15 green balls. a) What is the probability that a students selected at random from the group plays football given that he plays basketball?. Suppose a student is selected at random from the school. Find the probability that a randomly selected individual was a black female. What is the probability of a randomly selected student passing Mrs. The probability distribution of the random variable X,whereX denotes the number of questions answered correctly by a randomly chosen student, is represented by the accompanying histogram. Use appropriate notation and round to four decimal places. The table below shows the number of male and female students enrolled in nursing at a university for a certain semester. lexis wrote: If two students are chosen at random with replacement from a certain class, what is the probability that two male students or two female students are selected? (1) There are 50 male students in the class. A Detailed Explanation. Using Hypothetical Tables for Probability Example: Suppose that at a large high school, we know that 75% of the vehicles in the parking lot is an American-made vehicle and that 70% of the drivers are students. Numerade Educator 00:38. A card other than a 2 Find the probability of winning the lottery according to the given rules. There are 12 male seniors, 15 female seniors, 10 male juniors, 5 female juniors, 2 male sophomores, 4 female sophomores, 11 male freshmen and 12 female freshman. ¶lhat is the probability that a randomly selected student will go to college? What is the probability that a Yorktown student who goes to college is male? Given that a student has selected not to go to college, what is the probability that this Student is. Find the probablility that the person chosen at random. Use the table to determine the probability. that s a car is 065 and the probability o student a i' OR If the probability a both is 055. This table records the data. Left handed Right handed Total Male 3 29 32 Female 2 16 18 Total 5 45 50. What is the probability that at least two students share a common birthday month? (10) Nine balls are randomly withdrawn from an urn that contains 10 blue, 12 red, and 15 green balls. P(F|C) = ? Use the formula swapping F and C from the previous example: P(F|C) = P(F&C)/P(C) We have P(C) =. In this scenario, the marginal probability is not the same as the conditional probability. What is the probability that a female inmate was under 20 but not aged 16? Of those students playing musical instruments 60% were female. 06 (b) or or 90% or 0. statistics. A study of 400 randomly selected American Airlines flights showed that 344 arrived on time. Two students are to be picked at random to carry flags at the graduation. if a student being an out of state resident is independent of their gender, what is the probability of randomly selecting a female out of state resident at tech university?. The letters of the word “clamber” are scrambled and arranged in a random order. A student is selected at random. two females are selected. If a person is selected at random from the group, find the probability that the selected person is a teaching assistant or a female. If one student is. 23 HIV in Swaziland. Want to see this answer and more?. If a student is selected at random, find the probability that the student carries both a backpack and a wallet. a) randomly selected professor is a male and works for College of Humanities. Randomly selecting a person with type A blood Randomly selecting a person with type O blood c. population B. 2 Plays basketball only. What is the probability of the outcomes summing to five?. What is the probability that the rst die lands on a strictly higher alvue than the second die. Sports Teams. What is the probability that any randomly selected student (male or female) had a high school GPA between 2. What is the probability that there is a conflict in the student's schedule? iii) A committee of 5 students is selected a random from a group consisting of 10 boys and 5 girls. What is the probability that among the students in the sample exactly two are female?. Example: The distribution of 1237 college students by sex and major is given below. Probability sampling means that every individual in a population stands a chance of being selected. A card is randomly drawn from a standard deck of 52 cards. What is the probability that a book selected at random is a paperback, given that it is non-illustrated? ra. 70% of these female doctors are married. Among male birds of a species, 20% have a particular gene. Find the probability that a randomly selected person has been involved in an accident. Use the following information to answer the next four exercises. He pitches 50% of the games. Randomly select an undergraduate student who is taking a distance-learning course for credit, and record the student's age. 03 (a) Make a histogram of this probability distribution in the grid: zee (b) Describe P (X 3) in words and find its value. 363 while 57% of the workers at City Bank are female. Therefore, the probability that a right handed student selected at random is female is the fraction 1 2 2 5 0 , which to the nearest thousandth is 0. A) 4 7 B) 9 14 C) 5 6 D) 19 42 23. A study of 400 randomly selected American Airlines flights showed that 344 arrived on time. What is the probability that an “A” student is male? 5. What is the probability that a randomly selected student has a scaled test score of at least 90? (Ga. a) What is the probability that a randomly selected student is a female and lives off campus? b) What is the probability. Of all students with long hair, the probability that a student is female. given eight students, three of which are females, if two students are selected at random, without replacement, what is the probability that both students are female?. Using data from an undergraduate probability sample, we aimed to: (1) describe the prevalence and demographic characteristics of students who reported having engaged in rough sex with their current partner; (2) assess which sexual behaviors students consider to be rough sex; (3) describe the frequency with which participants report engaging in rough sex as well as their reports of initiating. Given that a randomly selected student is a sophomore, what is the probability that he/she is left-handed? What we know:. If one of these companies is selected at random (assume a 50-50 chance for each), and then a worker is selected at random, what is the probability that the worker will be female? A)10% B)57% C)52% D)47% 25) A bag. P(F|C) = ? Use the formula swapping F and C from the previous example: P(F|C) = P(F&C)/P(C) We have P(C) =. Let, z are the no of student who study both. to randomly select 40 US high school students who completed a survey. check_circle Expert Answer. The males comprise 40% of all the birds of the species (thus, females comprise 60%). Find the probability that a randomly selected individual was black; Find the probability that a randomly selected individual was a black or white male. There are 12 male seniors, 15 female seniors, 10 male juniors, 5 female juniors, 2 male sophomores, 4 female sophomores, 11 male freshmen and 12 female freshman. A student is randomly selected at tech university. 435 P(allergies) = 18/40 = 0. It deals the analysis of the frequency of past events. Continuous Random Variable: A continuous random variable, X , takes on all possible values in an interval (or a collection of intervals). The probability that a randomly selected student is a male student with short hair. P (M n S) is the probability that a randomly selected car has a manual transmission ð is a sedan. Binomial Probability Assume that male and female births are equally likely and that the births are independent. Snow's homeroom, what is the probability that the student is taking Algebra Il and Chemistry? Explain your reasoning. randomly selected student at this high school they had al least one family member living in house who smoked. Random or probabilistic : If an experiment, when repeated under identical conditions, do not produce the same outcome every time but the outcome in a trial is one of the several possible outcomes, then it is known as a random or probabilistic experiment. Ninety percent of the females attended college; 78% of the males attended college. 2) If a student is selected at random from Ms. What is the probability that a randomly selected person who tests positive for the predisposition by the test actually has the predisposition? one-quarter both female, and one-half are mixes: one male, one female. What is the probability that among the students in the sample exactly two are females? A. The heights (in. Education Male Female. 00 points At a certain university, 30% of the students major in zoology. Final members for research are randomly chosen from the various strata which leads to cost reduction and improved response efficiency. b) Find the probability that his/her grade is less than 50. Assume numbers are selected at random. What is the probability that a randomly selected female. 75 8 9 a) If a student is selected randomly, calculate the probability they are female. Find the probability of drawing the given card. 1)first two are boys and third is girl 2)first and third is of same gender and third is of opposite gender. What is the probability of the outcomes summing to five?. Out of the individuals over age 64, find the probability that a randomly selected individual was a black or white male. Define the random variabe Y to be the scaled score of a randomly selected student from the class. Two students are to be picked at random to carry flags at the graduation. Probability, Finite Mathematics: For the Managerial, Life, and Social Sciences 11th - Soo T. ate breakfast, if the student was a female 6. In stratified random sampling, or stratification, the strata. The males comprise 40% of all the birds of the species (thus, females comprise 60%). Let denote the event "the student is in the Computer Club. Ten of these students received an "A" for the final exam. Female 50 18 12 14 What is the probability a randomly selected person at the park is a female given that the person is under 40 years old? 60 167 60 81 A number line is shown below. Her results are shown below. 👍 Correct answer to the question A florist used 14 flowers to make a bouquet including 6 daisies what is the probability that a randomly selected flower will be a daisy - e-eduanswers. Valid discrete probability distribution examples.


text:
# An algebro-geometric theory of vector-valued modular forms of half-integral weight

-
Luca Candelori , LSU
IAS Room S-101

We give a geometric theory of vector-valued modular forms attached to Weil representations of rank 1 lattices. More specifically, we construct vector bundles over the moduli stack of elliptic curves, whose sections over the complex numbers correspond to vector-valued modular forms attached to rank 1 lattices. The key idea is to construct vector bundles of Schrodinger representations and line bundles of half-forms over appropriate `metaplectic stacks' and then show that their tensor products descend to the moduli stack of elliptic curves. We discuss extensions to the cusp at infinity and give an algebraic notion of q-expansions of vector-valued modular forms. We give algebraic notions of holomorphic vector-valued modular forms and cusp forms and compute algebraic dimension formulas for these spaces over any algebraically closed field of characteristic not dividing 2,3, by using the Riemann-Roch theorem for DM stacks. A special case of this theory can be used to give an algebro-geometric theory of modular forms of half-integral weight, as defined in the complex-analytic case by Shimura.

format: plain


text:
# What about apply maxplus algebra for all-pairs shortest paths?

I didn't find deep informations on Wikipedia about all-pairs shortest path, in particular I do not know what is the best algorithm to solve this problem beyond Floyd-Warshall's one, then I do not know if the following observation is too irrelevant or trivial.

In maxplus algebra we revisited linear algebra substituting the usual operations with the max-operation and plus-operation instead of addition and multiplication respectively. In particular we obtain an equivalent theory by taking minimum instead of maximum, then having a minplus algebra (with the obvious changing in the associated semiring, i.e. taking $+\infty$ instead of $-\infty$ as neutral element for the first operation).

Trying to see what the usual graph-theoretic-interpretation of matrix multiplication become in the minplus algebra (with $+\infty$ in the entries corresponding to non-existing edge and $0$s on the diagonal), I see that the $k$-th power of the adjacency matrix gives the shortest paths of length at most $k$. Then, all-pairs shortest path could be solved in $n^\omega \log n$ (where $\omega$ is the present lowest exponent for matrix multiplication) instead of $n^3$ like FW-alg.

Did I made big mistakes about all that?

I consider that maybe the lower bounds on matrix multiplication are not valid changing operations... but then seems plausible that it could be possible to have an exponent less than $3$ also for minplus algebraic matrix multiplication; among other things, the multiplication is far more computationally expensive than addition, and so is taking minimum respect to addition.

• the computational cost of multiplication of numbers does not matter much -- it's a cheap operation in this context. if you take a look at say Strassen's algorithm you'll realize that you need an additive inverse to make it work, but min is not invertible. APSP is actually just as expensive as min-plus matrix product (MPP), but we don't know how to do MPP faster than $O(n^3)$ either. However, there are matrix multiplication-based algorithms for special cases of APSP, see this and this – Sasho Nikolov Oct 20 '12 at 1:13
• @SashoNikolov thanks, this is a sufficient answer to my question. – Immanuel Weihnachten Oct 20 '12 at 1:40
• @SashoNikolov maybe convert to an answer ? – Suresh Venkat Oct 20 '12 at 3:25
• we don't know how to do MPP faster than $O(n^3)$ either — Actually, yes, we do! See these papers by Timothy Chan. (Admittedly, only polylog n faster, but still.) – Jeffε Oct 20 '12 at 3:37
• Very interesting. The Wikipedia article on APSP should be edited to include the fastest algorithm to solve it in general, that according to what is said here is to use the one by Timothy Chan. – Immanuel Weihnachten Oct 20 '12 at 19:46


text:
Indefinite Integrals of Trigonometric Functions

# Indefinite Integrals of Trigonometric Functions

The indefinite integrals for $\sin x$ and $\cos x$ should be rather easy to remember as we are just going in the opposite cyclic pattern for differentiation. Recall that the cycle of $\sin x \to \cos x \to -\sin x \to -\cos x \to \sin x \to ...$ is a good memory device for remembering the derivatives of a function. For example, the derivative of $\sin x$ is $\cos x$ (by following the arrows). For integration, the same mechanic works just in the opposite direction, so the antiderivative of $\cos x$ is $\sin x$. This information is summarized in the following property:

 Theorem 1: The following functions have the following indefinite integrals: a) If $f(x) = \sin x$, then $\int \sin x \: dx = -\cos x + C$. b) If $f(x) = \cos x$, then $\int \cos x \: dx = \sin x + C$. c) If $f(x) = \tan x$, then $\int \tan x \: dx = \ln \mid \sec x \mid + C$.

The indefinite integral for $\tan x$ is a little more complicated, and we cannot verify this integral yet. Let's look at some examples.

## Example 1

Evaluate the following integral: $\int 5 \cos x \: dx$.

From the Properties of Indefinite Integrals, and from the rules above, we can simplify this:

(1)
\begin{align} \int 5 \cos x \: dx \\ = 5 \int \cos x \: dx \\ = 5 \sin x + C \end{align}

## Example 2

Evaluate the following integral: $\int 4t^3 + \sin t \: dt$.

Once again, we will apply what we know:

(2)
\begin{align} \int 4t^3 + \sin t \: dt \\ = \int 4t^3 \: dt + \int \sin t \: dt \\ = \frac{4t^{4}}{4} -\cos t + C \\ = t^4 - \cos t + C \end{align}

## Example 3

Evaluate the following integral: $\int \frac{\sin x}{\cos x} + \tan x - x^\pi \: dx$.

Recall that $\frac{\sin x}{\cos x} = \tan x$, so it follows that:

(3)
\begin{align} \int \frac{\sin x}{\cos x} + \tan x - x^\pi \: dx = \int \tan x + \tan x - x^\pi \: dx \end{align}

Now we can integrate:

(4)
\begin{align} \int \tan x + \tan x - x^\pi \: dx \\ = \int 2 \tan x - x^\pi \: dx \\ = \int 2 \tan x \: dx - \int x^\pi \: dx \\ = 2 \int \tan x \: dx - \int x^\pi \: dx \\ = 2 \ln |\sec x | - \frac{x^{\pi + 1}}{\pi + 1} + C \\ \end{align}


text:
March 25, 2019
Press Releases
March 25, 2019
Games Press

If you enjoy reading this site, you might also want to check out these UBM Tech sites:

by Tommy Thompson on 12/03/18 10:16:00 am

The following blog post, unless otherwise noted, was written by a member of Gamasutra’s community.
The thoughts and opinions expressed are those of the writer and not Gamasutra or its parent company.

AI and Games is a crowdfunded YouTube series hosted on Patreon.  If you enjoy reading this piece please consider supporting the show at www.patreon.com/ai_and_games

In 2016 Tom Clancy's The Division brought players together in the war-torn streets of Manhattan fighting against a variety of enemy factions, as well as one another. Ubisoft's RPG-shooter carries a diverse range of enemies to keep the player on their toes. But unlike other games I've covered to-date, The Division needs to deal with the practical issues of being an online co-operative game and how to manage all sorts of AI systems for thousands of players across the world.

In this first of a two-part series, I'm going to be looking at how developers Massive Entertainment sought to create a variety of interesting and challenging encounters throughout the world of The Division; how they designed their enemy opponents and manage their behaviours as thousands of players rush to battle online every day in the mean streets of New York City.

# The Division

After an outbreak of weaponised smallpox, New York city breaks down into chaos and is quarantined from the outside world until the contamination is contained and order is restored. Players assume the role of an agent within the Strategic Homeland Division: a sleeper government unit that is activated in periods of national emergency in order to help first responders bring order to the region. Players can play individually or in groups of up to four completing a series of story missions and open world events in a region of Manhattan that at launch spanned over six square kilometres in size ranging from 21st street and 9th all the way to 55th and 3rd avenue.

To give players some variety and challenge, regions of the map are controlled by five rival factions: including the flamethrower-loving Cleaners, escaped convicts from Rikers Island, as well as the private military company the Last Man Battalion. In addition the most infected region of the city - The Dark Zone - has been cordoned off and is the games major PvP arena comprised of not only enemy AI but also fellow players who can go rogue at any time and begin to attack you.

As players explore the city of New York, they will interact with non-player characters (or NPCs) in one of three scenarios:

• As Roamers in the open world: such as a wild dog, pockets of civilians, friendly JTF soldiers near safe houses or hostile mobs out on patrol.
• Placed encounters: These are instances where players will find enemy mobs out in the game world, often deliberately positioned by the in-game systems with help from designers to force players into combat or to make an alternate route.
• Narrative missions: specific designer-crafted missions that are part of the main story of The Division. These are lengthy plot-driven sequences with an emphasis on glueing together multiple individual firefights.

In each instance, the AI placed in the world has specific objectives that are aligned with one of two critical design goals:

• To add to player immersion by enriching the in-game world and its design.
• To provide puzzles to solve in combat.

The latter was the critical part of the game: given it aims to encourage players towards scouting areas prior to combat and establishing a base level of strategy. Once fighting breaks out, players need to continually re-evaluate their combat priorities and spatial awareness in order to come out intact. This requires enemy NPCs to carry interesting behavioural traits for players to recognise, but also some consistency in their basic behaviours, with a variety of subsystems that handle threat detection, dynamic objective handling as well as being able to react to players themselves.

# The System

All NPC behaviours are achieved through use of a behaviour tree system, where subsections of the tree are activated to run specific behaviours that are seeded with certain objectives or variables. This can include the likes of target destinations for navigation, areas to explore potential threats, enemies to attack, cover to move into and so-on. I'm going to look at the design and structure of these for enemy NPCs, but if you want to learn more about how behaviour trees work: check out my articles on the AI of Halo 2 and 3 which cover some of this in more detail.

The behaviour tree architecture shown above (note: read from right to left) was reliant on a richly layered system, which was capable of providing multiple paths to each behaviour. This is because of the range of ways in which one specific action could arise and required the system to be as flexible as possible. The top layer of the tree [yellow-right] breaks down the three critical ways in which a NPC would react, including direct orders from in-game systems, to maintaining active combat or initiating combat if necessary. This moves down into the conditions layer [blue/purple-centre], which identifies what behaviours can be executed based on the current conditions of the world and the character itself, all the way down to the lower layer [left] which handles pretty much every variation of combat that is possible in the game.

What's critical here is that the middle layer is built such that it can link to a variety of different actions on the lower layer. This is to prevent behaviours being duplicated through the bottom half of the tree based on very specific conditions. As such all the different NPCs in the game (which I'll come back to in a minute), as well as tools such as the Seeker Mine - which is technically an AI character - can have similar sub-trees or behaviours to suit their purposes which are copied around. As you can imagine, this would result in a behaviour tree architecture that is rather complex - and you're right - what you see below is simply massive in scale and this required heavy collaboration between programming and design teams in order to get this working. Given the scale of the problem and the challenges faced, the programming team developed numerous tools for editing and eventually debugging each of the NPCs and built these into the Snowdrop engine that The Division is built upon. These debugging tools are extensive, given they allow for the developers to identify what is going wrong with a particular character in real-time in an online instance and I'll come back to talking about this later.

So now that we know a little more about the AI architecture, let's take a look at the design of the NPCs themselves.

# Archetypes & Factions

At launch The Division had 36 enemy NPCs types spread across five factions. Archetypes help establish the type of behaviour of a given character, while factions govern attributes that are specific to all NPCs within them. To enable a bit of gameplay diversity, there are large number of archetypes in The Division:

• Assault: Basic shooting and cover AI.
• Rusher: Rush directly towards target.
• Tank: Takes and deals large amount of damage.
• Sniper: Long-range and accurate assault.
• Thrower: Throw grenades and area-of-effect items.
• Support: Assist teammates in combat (e.g. healing)
• Heavy: Suppress players.
• Leader: Provide buffs to nearby players.
and
• Controller: Fights via Proxy (turret)

There are also Special NPCs that do not adhere to the archetypes model - but these are only used in end-game and boss battles.  Each of these archetypes are designed to give clear feedback of the immediate dangers to the player and how to strategise their attack patterns. In addition, many of these archetypes compliment one another (as shown in the image below) such that one can exploit each others attributes in order to achieving their goals.

For example, while snipers maintain their distance from players to deal large amounts of damage, rushers deal damage up close and immediately try to close the distance between themselves and the player. Meanwhile Tanks and Heavies force players to stay in cover, while throwers will attempt to flush players out. As such this forces players to use different tactics throughout a given battle based on the enemy unit composition. This is driven by a desire to force players to continually evaluate three key gameplay attributes:

• Target prioritisation and ordering: Who should I attack right now?
• Repositioning and exposure: Am I in the best cover given the current scenario? Often resulting in players moving to better tactic positions and keeping them from coming out of cover.
• Rewarding endurance: Provide long protracted battles that test a players ability to maintain their posture at a given level of intensity.

## Factions

As mentioned earlier, the 36 NPC types were spread across the major NPC factions: Rioters, Cleaners, Rikers and the Last Man Battalion that is split into tiers 1 and 2. Depending on where you are within the New York map, you will encounter one or more of these factions in combat. Each faction is designed to scale difficulty as you progress through the game, progressing in the order I listed them. But given there so many individual NPC types, how do you manage the difficulty progression in a manner that is easy for designers to iterate upon, but also effective enough to be pervasive across entire groups of NPCs.

To achieve this, Massive built an AI profile system that modifies a number of exposed attributes about each of the NPCs. This enables them to become more or less of a threat to the player accordingly. This are eight different attributes that are influenced here:

• Reaction time to player actions.
• Movement speed.
• Group behaviour
• Cover usage
• Skill usage
• Stagger resistance.
• Suppression resistance.
• Health
• Damage Accuracy

The profiles that are built can be consistent across either a specific NPC type or a faction that NPCs exists within. So for example the Rioters - who are the first faction in the game players will encounter - are restricted to using a 'Dumb' profile where all of these attributes are fairly low. However, all Heavy's, Support's and Turrets have dedicated profiles for those archetypes that are consistent across all factions. Meanwhile the Last Man Battalion have their own Elite profile: which makes them far more threatening to players than all others.

The last and final modifier that has an influence on an AI's behaviour is it's role and rank within the game itself. Characters range from regular grunts to veterans, elites and finally the named NPC rank, which is reserved for only the most high-priority targets. As a NPCs role increases, this has an influence on base stats such as weapon damage, armour and shot accuracy, with elite and named NPCs having access to unique weapons and mods. They even get custom laser sights that have absolutely zero effect on their gameplay ability, but it puts players on edge as a result.

# Closing

This suite of management systems enables Tom Clancy's The Division to build up a rigorous and diverse collection of non-player characters that help bring Manhattan to life. Whilst these systems fundamentally use the same core AI architecture, the use of archetypes, factions, profiles and ranks enable a lot of diversity in not just the behaviours executed, but also the level of challenge that these characters present for thousands of players across the world. But therein lies the bigger problem: how do you maintain performance for these kinds of systems in a game designed to run online for players all over the world? The Division has hosted over 10 million players since launch with a peak of over 1 million concurrent players. That's a lot of non-player characters that need to created, maintained and controlled over thousands of individual game instances.

In part 2 of my case study of The Division, I'm going to look at how Massive Entertainment pulled this off and explore the online integration. The design decisions that were made to ensure the game runs as smoothly as possible and the problems and limitations this presented for the AI systems. In addition, we'll also look at the tools that were built to enable testing of the AI behaviours in online instances, as well as how AI players were used to test the consistency and stability of story missions on test servers.

# Bibliography

• Jonas Gillberg, "AI Behaviour Editing and Debugging in Tom Clancy's The Division", Game Developers Conference (GDC), 2016.
• Drew Rechner & Philip Dunstan, "Blending Autonomy and Control: Creating NPC's for Tom Clancy's The Division", Game Developers Conference (GDC), 2016.
• Philip Dunstan, "How Tom Clancy's The Division Simluate Manhattan for Millions of Players", Nucl.ai 2016.

### Related Jobs

Pixel Pool — Portland, Oregon, United States
[03.22.19]

Software Developer (Unreal Engine 4, Blueprint, C++)
Crystal Dynamics — Redwood City, California, United States
[03.22.19]

Senior Tools Engineer
Sucker Punch Productions — Bellevue, Washington, United States
[03.22.19]

Open World Content Designer
Phosphor Studios — Chicago, Illinois, United States
[03.22.19]

Senior Gameplay Programmer


text:
# count¶

returns the total number of datapoints in the stream

Count represents the total number of datapoints passed through the transform. It is equivalent to an i used in a loop over an array, with the difference that count starts from 1, rather than 0.

No matter what the datapoints, the sequence of data that count returns is:

1,2,3,4,5...

## Usage¶

### Counting Mood¶

Suppose you want to count the number of times you were in a great mood:

where d >= 8 | count

The above transform will return only the datapoints where your mood rating was 8 or above, it will count them, and only return the last datapoint (which contains the full count).

### Counting Visits¶

Suppose you want to find how many times you visited a friend:

distance(<latitude>,<longitude>) < 50 | where changed | where d | count

The above transform finds when you were within 50 meters of the given coordinates (your friend’s home), filters these datapoints so only changes remain (so each time you visit, you get one true, followed by a false when you leave), filter the false values, and count the number of times you visited. Note that where d | count can be replaced with sum in this case.

### Counting Weekdays¶

Now you want to see which weekdays you use your computer the most. You can simply count the datapoints in your laptop’s stream to see what days have most data:

map(weekday,count)

### Transform Details¶

Input SchemaOutput Schema
{}

{
"type": "number"
}


text:
# Figure 2

 Elliptic (\vtwo, left) and triangular (\vthree, right) flow of \mbox{deuterons} as a function of \pt for different centrality intervals measured in \PbPb collisions at \snn~=~5.02~TeV. The horizontal line at zero is to guide the eye. Vertical bars and boxes represent the statistical and systematic uncertainties, respectively.


text:
# Rings of polynomials

The hypothesis of theorem 5.5 in page 152 of Hungerford's Algebra requires that the homomorphism maps the identity of R to the identity of S, but the proof "never" use this hypothesis. Is the theorem still true if the stronger hypothesis is removed. I am so sorry that I currently do not have link to the book.

Theorem 5.5 Let $R$ and $S$ be commutative rings with identity and $\varphi: R \to S$ a homomorphism of rings such that $\varphi(1_R) =1_S$. If $s_1, \dots, s_n \in S$, then there is a unique homomorphism of rings $\overline{\varphi}: R[x_1, \dots , x_n] \to S$ such that $\overline{\varphi}|R = \varphi$ and $\overline{\varphi}(x_i) = s_i$ for $i = 1,2, \dots, n$. This property completely determines $R[x_1, \dots, x_n]$ up to isomorphism.

-
@Yuan: You should really provide the text of the problem. – Arturo Magidin Jan 24 '11 at 22:18
Isn't it by definition that a ring homomorphism maps identities to identities for a CRWI? – PEV Jan 24 '11 at 22:19
@PEV: it is mutiplicative identity – Yuan Jan 24 '11 at 22:23
@PEV: It's a convention that many, but not all follow; if I recall correctly (not in my office right now), Hungerford does not require a ring homomorphism between rings with identity to restrict to a monoid homomorphism of the multiplicative monoids of the rings, but only a semigroup homomorphism (that is, a fancy way of saying Hungerford does not require ring homomorphisms between rings with identity to map the identity to the identity). – Arturo Magidin Jan 25 '11 at 3:27
@Arturo You're quite right. Hungerford explicitly says so in page 119 of his Algebra book. To quote him: "If $R$ and $S$ both have identities $1_R$ and $1_S$, we do not require that a homomorphism of rings map $1_R$ to $1_S$". – Adrián Barquero Jan 25 '11 at 4:10

The hypothesis is being stealthily used in the assertion that $\overline{\varphi}$ is a homomorphism of rings.

Added and rewritten: More explicitly: the sketch Hungerford provides is to take an element of the polynomial ring $$\sum r_{i}x_1^{k_{1i}}x_2^{k_{2i}}\cdots x_n^{k_{ni}}$$ (suitably finite) and suggests mapping it to $$\sum\varphi(r_i)s_1^{k_{1i}}\cdots x_n^{k_{ni}}.$$ Then Hungerford asserts that this makes $\overline{\varphi}$ into a ring homomorphism.

You don't actually need the full hypothesis that $\varphi(1_R)=1_S$, but you do need something:

For $\varphi$ to be a ring homomorphism, we need $\varphi(1_R)$ to be an identity for $\varphi(R)$; for $\overline{\varphi}$ defined as above to be a ring homomorphism, we also need $\varphi(1_R)s_j = s_j$, because taking $p = 1_R$ and $q=x_j$ we have $\overline{\varphi}(pq) = \overline{\varphi}(x_j) =s_j$, and $\overline{\varphi}(p)\overline{\varphi}(q) = \varphi(1_R)s_j$. Thus, for $\overline{\varphi}$ to be a ring homomorphism, it is necessary that $\varphi(1_R)$ be an identity of the subring of $S$ generated by $\varphi(R)$ and $s_1,\ldots,s_n$ (as $R$ and $S$ are both commutative).

In fact, this is also sufficient for you to be able to get a homomorphism: you must require that $\varphi(1_R)$ be the identity for the subring of $S$ generated by $\varphi(R)$ and $s_1,\ldots,s_n$.

But it is not hard to check that the apparently weaker condition in the theorem (weaker, because it refers to a smaller class of homomorphisms and possible selections of $s_1,\ldots,s_n$) is in fact sufficient to characterize the polynomial ring up to unique isomorphism; the theorem suffices to prove the more general case by considering first the map onto $S'=\langle \varphi(R),s_1,\ldots,s_n\rangle$ and then composing with the embedding $S'\hookrightarrow S$ (since we are not requiring maps of rings with identity to send the identity to the identity).

-
Could you please explain "completely determine" means in this theorem? I feel confused about it. – Yuan Jan 27 '11 at 4:43
@Yuan: It means that any commutative ring with identity $T$ and elements $t_1,\ldots,t_n$, together with an embedding $i\colon R\to T$, which satisfies the hypothesis of the theorem (for every homomorphism $\varphi\colon R\to S$ with $\varphi(1_R)=1_S$ and every elements $s_1,\ldots,s_n\in S$ there exists a unique homomorphism $\overline{\varphi}\colon T\to S$ such that $\varphi=\overline{\varphi}\circ i$ and $\overline{\varphi}(t_j)=s_j$, will be isomorphic to the ring of polynomials, and the isomorphism will be canonical. It's a typical category-theory statement about universality. – Arturo Magidin Jan 27 '11 at 5:10