(adsbygoogle = window.adsbygoogle || []).push({}); 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 n^{th}moment (E|X|^{n}<inf) for all positive integers n

2. Relevant equations

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

3. 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.

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# Probability- finite n-th moment

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