Hi. I need some help verifying something.
Let X, Y be discrete random variables such that 1<=X,Y<=10. Then:
Thanks in advance.
Coincidentally, I just came across the formal statement of this recently in another thread on interestingly named math concepts. It is true, and sometimes known as the law of the unconscious statistician.
This isn't your question, but a word of caution on something semi-related: It is not correct to do things like E(|X-Y|) = |E(X)-E(Y)|.