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Math Help - help needed

  1. #1
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    help needed

    please help me solve this one:

    Let Ti be the number of trials up to and including the ith success.
    Let Nn be the number of successes in the first n trials. show that
    P(T1=x|Nn=1)=1/n x=1,2,...n
    thanks.
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  2. #2
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    Quote Originally Posted by adirh View Post
    please help me solve this one:

    Let Ti be the number of trials up to and including the ith success.
    Let Nn be the number of successes in the first n trials. show that
    P(T1=x|Nn=1)=1/n x=1,2,...n
    thanks.
    T_1 ~ Geometric(p).

    N_n ~ Binomial(n, p).

    Therefore \Pr(N_n = 1) = n p (1 - p)^{n-1} and \Pr(T_1 = x \cap N_n = 1) = (1 - p)^{x-1} p \cdot (1 - p)^{n-x}.
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