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Math Help - Poisson Distribution

  1. #1
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    Poisson Distribution

    Let X have Poisson distribution. Calculate:

    a) E(3X+5)
    b)Var(3X+5)
    c) E(1/(1-x))

    Can you assume independence and use the additive/distributive properties? I don't understand which equation I am supposed to be using...
    Thank you!!!
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  2. #2
    Moo
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    Hello,

    well, if you want to be complicated... any random variable is independent with any constant.

    But for the first question, you just have to use the linearity of the expectation : E(aX+b)=aE(X)+b, where a and b are constants.

    For the second question, Var(aX+b)=aČVar(X), because Var(constant)=0, and if you don't see why, go back to the definition of the variance.

    For the last question, is it x or X ?
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  3. #3
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    It's X and THANK YOU!!!!

    It's big X
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  4. #4
    MHF Contributor matheagle's Avatar
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    I can calculate E(1/(1+X)), but I have trouble with E(1/(1-X)).
    The part where x=1 in the series causes trouble.
    It's 3am and I'm tired.
    I need to revise one paper, work on an example or two on another and continue with the simulations on a third paper.
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