Let $X_1,X_2,...;X_n$ be a random sample with $X_i$~$Binomial(m,p)$ for $i=1,...,n$ and $m=1,2,3,...$ and let $p\in (0,1)$. We assume $m$ is known and we are given the following data $x_1,...,x_n\in\{0,...,m\}$
Write up the log-likelihood function and find the MLE $\hat{P}ML$ for p
I'm not quite sure how to approach this. This is what I've tried:
I believe the likelihood function of a Binomial trial is given by
$P_{X_i}(x;m)=$ ${m}\choose{x} $$p^x(1-p)^{m-x}$
From here I'm kind of stuck. I'm uncertain how I find/calculate the log likelihood function.
I've understood the MLE as being taking the derivative with respect to m, setting the equation equal to zero and isolating m (like with most maximization problems). So finding the log likelihood function seems to be my problem
Edit: I might be misunderstanding it but could the log likelihood function simple be log of the likelihood function? so $log(P_{X_i}(x;m))$