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    Determine distribution given moment generating function




    I am given two moment generating functions, and need to calculate some probabilities regarding them.

    The first is: M(t) = ((2/3)e^t + (1/3))^3

    I recognized this to be a binomial distribution with n = 3 and p = 2/3

    The second is: M(t) = (1/3) + (1/6)e^{6t} + (1/2)e^{2t}

    I am having trouble figuring out what distribution this follows (is it also a binomial distribution, just not simplified? If so, how would one simplify it?)

    Any help would be greatly appreciated!

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    Re: Determine distribution given moment generating function


    Do you know the relationship between a discrete random variable’s moment-generating function and its probability-generating function, and that the latter can be used to calculate probabilities?

    Your second moment-generating function is not a standard type or a convolution of standard types, but you can still calculate probabilities of discrete events from it.

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