Determining Limiting Distribution

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

    Let Xn have a gamma distribution with parameters alpha = n, and beta, where beta is not a function of n. Let Yn = Xn/n. Find the limiting distribution of Yn.

    2. Relevant equations

    3. The attempt at a solution

    [tex]E(e^{tY_n}) = E(e^{t\frac{X_n}{n}})[/tex]

    I'm stuck here. I know that the MGF of a gamma distribution (in this case) is [tex](1-\beta t)^{-n}[/tex]

    I'm not sure with what to do about the 1/n in the MGF. Would it be just [tex]\frac{(1-\beta t)^{-n}}{n}[/tex]

    Any help would be appreciated.
    Last edited: Oct 19, 2009
  2. jcsd
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