For a nonnegative integer-valued discrete random variable X, show that

E(X)=http://upload.wikimedia.org/math/3/d...c702e182f0.pngx=0 (to infinity) P(X>x). Can anyone help me solve this please?

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- Mar 17th 2009, 10:43 PMblues360Proof for mean of non-negative discrete random variable
For a nonnegative integer-valued discrete random variable X, show that

E(X)=http://upload.wikimedia.org/math/3/d...c702e182f0.pngx=0 (to infinity) P(X>x). Can anyone help me solve this please? - Mar 18th 2009, 09:03 AMmeymathis
So

This is a triangular region. So we can switch the order of the sum if we do it carefully.

Can you finish it? - Mar 18th 2009, 06:03 PMblues360
Thank so much for your reply!

So to finish it then:

http://www.mathhelpforum.com/math-he...b874ace9-1.gif=http://upload.wikimedia.org/math/3/d...c702e182f0.pngx=0 (to infinity)xP(x)=E(x)?

Because x=0 --> y=1? - Mar 18th 2009, 09:12 PMmeymathis
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