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Probability- finite n-th moment

  1. Oct 10, 2010 #1
    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=[tex]\sum[/tex]([tex]\frac{x^n}{(n!)}[/tex], 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) < [tex]\sum[/tex]([tex]\frac{x^n}{(n!)}[/tex]

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

    would appreciate any help.

    Thanks.
     
  2. jcsd
  3. Oct 10, 2010 #2
    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.
     
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