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Proof convergence
Posted:
Mar 20, 2010 10:25 AM


Hi,
I have problems with a proof I should show. I should show that, given X a r.v. >=0, then the expected value E(X)<inf iff sum_(i>=1)P(X>i)<inf.
I tried out different way, but I don't get how to solve this problem. Starting from the expected value formula, I get stuck already at sum_(i>=1)(P(x=i)*i)<inf (don't knowing how to proceed). If I start at the other side, I get (for descrete n): sum_{i>=1}(sum_{j>=i}(P(x=j)))<inf
I really don't know how I can proof this statement, even though I do understand its meaning...
Please help me,
Thanks in advance :)



