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Math Help - true or false???

  1. #1
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    true or false???

    if x distributed as Poisson distribution with parameter lambda=5 find:

    1- moment generating function of (3x-2)
    2- the mean and variance of (-4x-6)
    3- the moment generating function about the origin

    solutions :
    (1) {e ^(-2t)} * {e^((5e^3t)-5)}

    (2) mean = -26 & variance = 80

    (3) 30
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  2. #2
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    Quote Originally Posted by flower3 View Post
    if x distributed as Poisson distribution with parameter lambda=5 find:

    1- moment generating function of (3x-2)
    2- the mean and variance of (-4x-6)
    3- the moment generating function about the origin

    solutions :
    (1) {e ^(-2t)} * {e^((5e^3t)-5)} Mr F says: Correct, since if X has moment generating function m(t) then (it can be easily shown that) aX + b has moment generating function {\color{red} e^{bt} \, m(at)}. And you have m(t) from question 3.

    (2) mean = -26 & variance = 80 Mr F says: Correct, since E(-4X - 6) = -4 E(X) - 6 and Var(-4X - 6) = 16 Var(X).

    (3) 30 Mr F says: Wrong. {\color{red}m(t) = e^{5(e^t - 1)}}.
    The proof of the result given in (3) can be found in this thread: http://www.mathhelpforum.com/math-he...tribution.html
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  3. #3
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    thank you >>>

    (3) the second moment about the origin " my question is false but my answer i think true "
    = 30
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