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    Finding probability from Moment Generating Functions




    I am stuck on part 3 of this question.

    I am given the following moment generating function mx(t) e^(4e^t-4)

    1) identify the distribution and parameters.

    I have found that it is a Poisson distribution with alpha =4.

    2) Determine the mean and variance:
    Although i didn't need to do so with this problem, i went ahead and found the first moment and second moment got E[X]=4 and V[X]=4

    3) Determine Pr(X>3) This is the part that i am stuck on. Not sure how to proceed. Do i integrate? and if so what do i integrate and what are the limits? Thank you.

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    Re: Finding probability from Moment Generating Functions

    You've identified the distribution. Forget about the moment generating function. What is Pr(X>3)?
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    Re: Finding probability from Moment Generating Functions


    The poisson distribution is discrete so there is nothing to integrate. Try to find the complement of P(X>3).

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