So, the question/problem I have is this: Prove that the Cov(x,x) = Var(x)
I had the idea to use the definition of cov(x,y) = sum all x sum all y of (x-E(x))(y-E(y))p(x,y), and by plugging in x for y i would then have two sums over all x of (x-E(x))^2 * p(x,x)
the definition of var(x) is the sum over all x of (x-E(x))^2 * p(x)
is it okay to say that p(x,x) = p(x)?
Also, how do i get rid of that second summation?
Thanks!!