Estimation

Let $X_1, \dots, X_n$ be i.i.d. with $\mathbb{P}(X = k) = (1 - p)^{k-1}p$, $k = 1, 2, \dots$ (a) Find a sufficient statistic. (b) Find the MLE of $p$. (c) Find $I(p)$ and the Cramér–Rao bound.