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Math Help - Square root of Poisson Distribution

  1. #1
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    Square root of Poisson Distribution

    Let  Y_n be a sequence of Poisson distributed random variables with mean n*u. Let  X_n =  {Y_n}^{1/2} . Find the limiting distribution of  X_n after properly standardized.

    I'm pretty sure that X should be normally distributed and the answer should use the CLT in some way. All I have so far is that:

     P(X=x) = \frac{e^{-nu}(nu)^{x^2}}{{x^2}!}

    And now i'm pretty much stuck
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  2. #2
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    Quote Originally Posted by southprkfan1 View Post
    Let  Y_n be a sequence of Poisson distributed random variables with mean n*u. Let  X_n = {Y_n}^{1/2} . Find the limiting distribution of  X_n after properly standardized.

    I'm pretty sure that X should be normally distributed and the answer should use the CLT in some way. All I have so far is that:

     P(X=x) = \frac{e^{-nu}(nu)^{x^2}}{{x^2}!}

    And now i'm pretty much stuck
    Is this relevant: http://www.tina-vision.net/docs/memos/2001-010.pdf
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    Thanks for the link, but I didn't really find it helpful (or maybe it's just late and I'm tired). It also appears to take a lot of information for granted.
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