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Math Help - Convergence in probability

  1. #1
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    Convergence in probability

    Hi I have a question:

    So suppose that
    P(Yn = k) = (1 - 2-n-1)-1 / 2k+1 for k=0,1,...n.
    And Y~ geo(1/2)
    How do I show that Yn converges in distribution to Y?

    I know I have to incorporate the PMF of the geometric distribution which is px(k) = P(X=k) = (1-p)k-1p
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  2. #2
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    Re: Convergence in probability

    Convergence in probability and convergence in distribution are two different thing. If you are in fact meant to show CID, all you need to do is - for an arbitrary k - show that P(Y_n = k) = 1/2^(k+1) as n goes to infinity, which really shouldn't be that hard.

    To show CIP , you need to state what the r.v. Y_n is meant to converge to (for example the sample mean converging to the population mean).
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