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    Let X1,X2... be a sequence of independent and identically distributed continuous random variables. Define the random variable ...
    (a) Compute the p.m.f of N by first computing P(N [less than or equal to] n)
    (b) Show that E(N)=e

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    © BrainMass Inc. brainmass.com March 4, 2021, 6:06 pm ad1c9bdddf
    https://brainmass.com/statistics/probability/continuous-random-variables-independent-factors-28958

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    First, we need to find the probability that . Since are independent and identically distributed continuous random variables, by symmetry, we know that
    and . So,

    Secondly, we know ...

    Solution Summary

    Let X1,X2... be a sequence of independent and identically distributed continuous random variables. Define the random variable ...
    (a) Compute the p.m.f of N by first computing P(N [less than or equal to] n)
    (b) Show that E(N)=e

    $2.49

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