For a nonnegative integer-valued discrete random variable X, show that
E(X)=x=0 (to infinity) P(X>x). Can anyone help me solve this please?
Well, there are no x's anymore. The x and y are just the summing variables.
The main observation at this point is that the sum:
almost is (whether it is x or y doesn't matter, it is just a summing variable). The only thing missing is the 0 term. The sum should go from 0 to , whereas this one starts at 1. But the 0 term is
.
So