The moment generating function of a random variable $X$ is given by:

$$M(t) = (1/3^{2k})(7+2e^t)^k, \quad \forall t$$

a) Determine $P(X = 3)$

b) Derive the $r^{th}$ factorial moment of $X$

I assume you must deduce what distribution this is from the mgf, I just have no idea which one it is.


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