The expected value of a random variable is its mean
The variance of a random variable is its second central moment.
since,
what do you get???
If X is a discrete random variable and E[X] exists and the function given by f(x) for each x in the domain of the function is the probability mass function at x, then
VAR[x]=E[x^2] - (E[x])^2
Im confused on what im suppose to satisfy for the hypothesis. i know the claim is true by trial and error, but can i just pick any discrete function and show it (solved it using a bernoulli) ? or do i have to show it for all functions which i don't know how to do.
This is a standard proof. Here it is on wiki
Variance - Wikipedia, the free encyclopedia