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Math Help - …find the moment generating function????

  1. #1
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    Exclamation …find the moment generating function????

    If E[X^r] = 6^r
    where r = 1, 2, 3...

    …can you please help me find the moment generating function and the p.m.f. of X?
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  2. #2
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    Quote Originally Posted by Intsecxtanx View Post
    If E[X^r] = 6^r
    where r = 1, 2, 3...

    …can you please help me find the moment generating function and the p.m.f. of X?
    From the definition of the moment generating function it should be clear that

    M_X(t) = 1 + 6t + \frac{6^2}{2!} t^2 + .... + \frac{6^n}{n!} t^n + .... = \sum_{k = 0}^{+ \infty} \frac{(6t)^k}{k!}

    and you should recognise what this function is. Then it should be clear that M_X(t) is the mgf of a pmf that has all its mass concentrated at one point. That is, p(x) = 1 when x = c and the value of c is obvious.
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