# Finite expectation value <-> finite sum over Probabilties

1. Nov 23, 2007

### Mr.Brown

1. The problem statement, all variables and given/known data
If X is a real valued random variable with E[|X|] finite. <-> $$\sum(P(|X|>n))$$ finite

, with the sum over all natural numbers from 1 to infinity.
2. Relevant equations

As a tip Im given that for all integer valued X>0 E(X) = $$\sum(P(X)>k$$ , where the sum goes over all k =1 to k=infinity (k is a natural number)

3. The attempt at a solution

I don´t really have an idea i tried to find a way to relate integer valued stuff to real valued stuff by summing over all real valued stuff that are not integer.
But dont get anywhere :(
Hope for some advice

2. Nov 23, 2007

### EnumaElish

What is the formula for E[|X|]?

3. Nov 24, 2007

### Mr.Brown

It´s just the expectation value E[|X|]= sum over all |x|*P(|x|).

4. Nov 24, 2007

### Mr.Brown

ok solved it :)