- #1
Roni1985
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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 nth moment (E|X|n<inf) for all positive integers n
Homework Equations
ex=[tex]\sum[/tex]([tex]\frac{x^n}{(n!)}[/tex], n,0,inf)
The Attempt at a Solution
we know that E(et*x) < infI can use the Taylor expansion but I end up with
E(et*x) < [tex]\sum[/tex]([tex]\frac{x^n}{(n!)}[/tex]
don't know how to pick up from here...
would appreciate any help.
Thanks.