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Math Help - help with random variable convergence

  1. #1
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    help with random variable convergence

    P(Yn=k)= ( (1-2^(-n-1))^(-1) )/ 2^(k+1) for k=0,1,2,...,n. The random variable Y has the geometric distribution where lambda is 1/2. How can I prove that {Yn} converges in distribution to Y?


    Any help is appriciated.


    I get fY(y)=1/2^(y+1)
    but how do I prove the convergence?
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  2. #2
    MHF Contributor matheagle's Avatar
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    what does ( (1-2^(-n-1))^(-1) )/ 2^(k+1) mean?
    I know that 1-2=-1, but I doubt you meant that.
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  3. #3
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    ok i figured it out, and i dont know where you got 1-2 from, that part was not in the equation in my first post... well the term 2 had an exponential, which is what you might have not seen.
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