Finite expectation value <-> finite sum over Probabilties

[Mr.Brown]

Homework Statement

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.

Homework Equations

As a tip I am 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)

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 don't get anywhere :(
Hope for some advice

 

[EnumaElish]

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

 

[Mr.Brown]

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

 

[Mr.Brown]

ok solved it :)