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Math Help - limiting distribution

  1. #1
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    limiting distribution

    Let X1,....,Xn be a random sample from a Poisson( \lambda) distribution.

    Find the limiting distribution of \overline{X^2}.

    I found the mean to be E( \overline{X^2}) = (1/n)*E(X_i)^2

    but then i don't know which method to use.

    Thank you
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  2. #2
    MHF Contributor matheagle's Avatar
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    The square is a continuous function.

    Since \bar X\to \lambda

    we have \left(\bar X\right)^2\to \lambda^2


    and I don't understand what this.... (1/n)*E(X_i)^2 means
    I guess zero as n goes to infinity
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