Prove finite expectation value

[someone]

Hallo,

I've got a problem with a proof:

I should prove that a r.v. X (>=0) has a finite expectation value iff
sum_{i>=1}P(X>i) is finite.

I tried it in different ways but always get stuck when I come to:
sum_{i>=1}P(X=i)*i < inf
or, if I start at the second part (for discrete i) at:
sum_{i>=1}sum_{j>=i}P(X=j) < inf

But I am not able to combine these two statements in order to prove the original one
Please, can someone help me?

Thanks in advance

[mp83]

Check this.

> http://en.wikipedia.org/wiki/Expecte...egative_values

> http://statsravingmad.wordpress.com/?s=darth