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Math Help - convergence problem on random variables

  1. #1
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    Angry convergence problem on random variables

    Suppose P(Yn<=y)=1-e^(-2ny/(n+1)) for all y>0. Prove that Yn converges in distribution to Y where Y has the exponential distribution for some lambda >0 and compute lambda.

    so for this i get
    [lim n->inf] 1-e^(-(2ny)/(n+1)) -> 1-e^(-y*lambda)

    I'm not sure how to prove the convergence here...
    Is it enough to say that lambda = (2n)/(n+1) ?
    since 2n > n+1, the result will always be > 1, which is what lambda can be.
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  2. #2
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    What is the limit of \frac{n}{n+1}? Why is \lim e^{x_n}=e^{\lim x_n}?
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  3. #3
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    nvm i figured it out, lambda = 2
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