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    help with convergence of 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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    Re: help with convergence of random variables


    I think it is alright.

    But you also need to know

    \lambda = \lim_{n\to\infty} \frac {2n} {n+1}
= \lim_{n\to\infty} \frac {2} {\displaystyle 1 + \frac {1} {n}}
= \frac {2} {1 + 0} = 2

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