# Probability- finite n-th moment

1. Oct 10, 2010

### Roni1985

1. The problem statement, all variables and given/known data

Suppose the random variable X has finite exponential moment. Show by comparison to the Taylor series for EXP[x] that X has finite nth moment (E|X|n<inf) for all positive integers n

2. Relevant equations

ex=$$\sum$$($$\frac{x^n}{(n!)}$$, n,0,inf)

3. The attempt at a solution

we know that E(et*x) < inf

I can use the Taylor expansion but I end up with

E(et*x) < $$\sum$$($$\frac{x^n}{(n!)}$$

don't know how to pick up from here...

would appreciate any help.

Thanks.

2. Oct 10, 2010

### Roni1985

sorry for the bump, it's really important for me :\ have an exam in two days and I've been trying to solve it since 12 pm.

Thanks.