Math 6010 • Linear Models

Let \(X_1,X_2,\ldots,X_n\) be independent identically distributed random variables with \(P\{X_i=1\}=p\), \(P\{X_i=0\}=1-p\).
\begin{parts}
\item Compute the maximum likelihood estimator of \(\sigma^2=p(1-p)\).
\item Compute the bias, the variance and the mean-square error of the estimator.
\item Is the estimator asymptotically efficient?
\item Find the uniformly minimum variance unbiased estimator for \(\sigma^2\).
\end{parts}