Suppose that $X_1, X_2$, and $X_3$ are identically distributed independent discrete random variables with probabilities given by...
- $1/3$ if $x=0$
- $2/3$ if $x=1$
- $0$ else
Find the moment generating function of $Y=X_1X_2X_3$
So far, I have the following
$\sum \exp(Yt)\cdot p(Y)$
but I have no idea where to go from there.