# Math Help - Probability Distributions

1. ## Probability Distributions

1) Verify f(x) = (2x)/(k(k+1)) for x = 1,2,3,...,k can serve as the probability distribution function of a random variable with the given range.

I know this has to satisfy two parts. I got the first part, where for each value in the domain, f(x) >= 0. I am having trouble with the part where the sum has to equal 1. How do I show this?

2. Hello,
Originally Posted by noles2188
1) Verify f(x) = (2x)/(k(k+1)) for x = 1,2,3,...,k can serve as the probability distribution function of a random variable with the given range.

I know this has to satisfy two parts. I got the first part, where for each value in the domain, f(x) >= 0. I am having trouble with the part where the sum has to equal 1. How do I show this?
$\sum_{x=1}^k f(x)=\sum_{x=1}^k \frac{2x}{k(k+1)}=\frac{2}{k(k+1)}\sum_{x=1}^k x$

and the sum of the first k integers is $\frac{k(k+1)}{2}$