If $X$ is $poisson(\lambda)$, find the MGF of $X$. (Enter $\lambda$ as $l$)
$M(t)=$

Hint:

If $\lambda = 5$, differentiate the MGF you found above to find the first 3 moments of $X$ about 0.
1st Moment:
2nd Moment:
3rd Moment:
Using the moments above, calculate the variance of $X$.
$var(X)=$

Hint: