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Probabilty help please!

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    If x1~geometric(0.2) and x2~(0.4) what is the moment generating function of 2x1+4x2 and does 2x1+4x2 have geometric distribution?

    (Original post by Harriettttttt1)
    If x1~geometric(0.2) and x2~(0.4) what is the moment generating function of 2x1+4x2 and does 2x1+4x2 have geometric distribution?
    So the definition of the moment generating function is

     \displaymode M_X(t) = \mathbb{E}(e^{tX})

    If you do the sums you will find that for a geometric distribution with parameter p, this is

     \displaymode M_X(t) = \frac{p e^t}{1 - (1-p)e^t}

    (provided that you're using the geometric distribution with support on the strictly positive integers)

    To answer the next part, how do you work out the moment generating function of aX + bY (a, b integer constants) from those of X & Y? You should know a theorem that helps you with this. Then finally, is the MGF that you obtain in the form of the MGF of some geometric distribution?
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