- #1

Roni1985

- 201

- 0

## Homework Statement

Suppose the random variable X has finite exponential moment. Show by comparison to the Taylor series for EXP[x] that X has finite n

^{th}moment (E|X|

^{n}<inf) for all positive integers n

## Homework Equations

e

^{x}=[tex]\sum[/tex]([tex]\frac{x^n}{(n!)}[/tex], n,0,inf)

## The Attempt at a Solution

we know that E(e^{t*x}) < inf

I can use the Taylor expansion but I end up with

E(e

^{t*x}) < [tex]\sum[/tex]([tex]\frac{x^n}{(n!)}[/tex]

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

would appreciate any help.

Thanks.