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Thread: Time scaling a geometric random variable

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    Re: Time scaling a geometric random variable




    One last question, how would you define the pmf of the scaled r.v. ?

    i.e. the original r.v. has the pmf given by: P(X = x) = (1 - p)^{x-1} p

    What is the pmf P(Y= y) where Y = N * X?

    Is it: P(Y = N x) = (1 - p)^{N x - 1} p

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    Re: Time scaling a geometric random variable

    They have the correct pmf in equation 4.5. The issue was that instead of calculating E[X] they were calculating E[X/h] and Var[X/h]. They did a bad job with their notation.
    I don't have emotions and sometimes that makes me very sad.

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    Re: Time scaling a geometric random variable

    In equation 4.5, is ph = N / p?

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    Re: Time scaling a geometric random variable


    ph is the success probability for what they call a single 'trial group'. This is the same as your p where you just have trials with success probability 'p' that take place every N units in time.
    I don't have emotions and sometimes that makes me very sad.

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