…find the moment generating function????

**Intsecxtanx** · October 3rd 2009, 01:56 PM

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?

**mr fantastic** · October 3rd 2009, 11:39 PM

Originally Posted by Intsecxtanx

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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