This problem was part of an assignment in my undergrad stats class.
Suppose Steph Curry takes ten 3-point shots per game, and the number of 3-point
shots scored follows a $𝐵𝐼𝑁\sim(10, 𝑝)$ distribution, where 𝑝 is the probability of successfully
scoring a 3-point shot. [Note: in basketball a 3-point shot is one taken from behind the 3-
point arc]. To estimate this probability, a random sample of 10 games is considered and
the number of successful 3-point shots is recorded. These data are shown below.
$$\begin{array}{ccccc} \hline 5 & 3 & 0 & 7 & 10 \\ 2 & 4 & 6 & 8 & 1 \\ \hline \end{array}$$
Calculate the maximum likelihood estimate, $\tilde{p}_{ML}$, of $p$, the probability of scoring a 3- point shot, and verify (using either the first or second derivative test) that you have found a maximum.
So I've $X\sim BIN(10,p)$
I go through the steps to find the estimator and arrive at
\begin{equation} \sum_{i=1}^{10}x_i(1-p)=p\sum_{i=1}^{10}(10-x_i) \end{equation}
I'm at a standstill in how I solve for $p$. Then when I have the estimator, do I do anything with the provided info in the table? any help would be appreciated