Moment generating function (find the probability)

Asked 3 months ago

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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.

Vizag

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asked May 8 at 13:14

KombatWombat

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$\begingroup$ Hint: put the $1/9^k$ into the other brackets so the MGF is $\left(\frac{7}{9}+\frac{2}{9}e^t\right)^k$. If you're still unsure, see math.stackexchange.com/questions/236636/…. $\endgroup$ – Minus One-Twelfth May 8 at 13:23

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