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Topic: Proof convergence
Replies: 1   Last Post: Mar 20, 2010 12:03 PM

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someone123

Posts: 1
Registered: 3/20/10
Proof convergence
Posted: Mar 20, 2010 10:25 AM
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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 :)


Date Subject Author
3/20/10
Read Proof convergence
someone123
3/20/10
Read RE: Proof convergence
Ben Brink

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