<transcript><audio_8>their three boundary copulas also known as the simplest populous and the one that we've already come across specifically in the traduction video was the independent copula and this basically says if two probabilities have</transcript><caption><image_9>The image is a screenshot of a mathematical equation written in red and blue text. The equation is written in a neat and organized manner, with the title "Mathematical-Mailing-Innovation-Symbol" at the top. Below the title, there is a list of mathematical equations written in black text. 

The equations are arranged in a table format, with each equation having its own set of numbers and symbols. The first equation is for a mathematical problem, and the second equation is to find the value of the equation. The third equation is from a mathematical formula, and it is written as a mathematical representation of the mathematical equation.

At the bottom of the image, there are two bullet points, one for the equation and the other for the problem. The bullet points are written in blue text, and they appear to be related to mathematical equations. The background is white, and there is no other text or images in the image.</caption><transcript><audio_10>absolutely zero dependency thus they are independent we simply multiply the two together in order to create the joint distribution and this is something like I said we should be very very familiar with from learning statistics in first</transcript><transcript><audio_11>and second Jeff if you're watching this course and you haven't done first and second yeah statistics I highly recommend you do that first otherwise the statistics here is going to get a little bit more intense then we have the second copy that I want to talk</transcript><transcript><audio_12>about something known as the minimum copula and this idea is that the the copula function between f of X and f of Y is simply going to be the smaller of the two the minimum value and we also</transcript><transcript><audio_13>have something known as the maximum copula which says you know the Joint Distribution between two marginal distributions is sometimes the maximum of of the two so minimum and maximum are probably a little bit harder to</transcript><transcript><audio_14>comprehend in the independent copula so we are going to talk a little bit more about them but essentially they all relate to dependency so when we have zero dependency we have the independent</transcript> their three boundary copulas also known as the simplest populous and the one that we've already come across specifically in the traduction video was the independent copula and this basically says if two probabilities have absolutely zero dependency thus they are independent we simply multiply the two together in order to create the joint distribution and this is something like I said we should be very very familiar with from learning statistics in first and second Jeff if you're watching this course and you haven't done first and second yeah statistics I highly recommend you do that first otherwise the statistics here is going to get a little bit more intense then we have the second copy that I want to talk about something known as the minimum copula and this idea is that the the copula function between f of X and f of Y is simply going to be the smaller of the two the minimum value and we also have something known as the maximum copula which says you know the Joint Distribution between two marginal distributions is sometimes the maximum of of the two so minimum and maximum are probably a little bit harder to comprehend in the independent copula so we are going to talk a little bit more about them but essentially they all relate to dependency so when we have zero dependency we have the independent
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