In: Statistics and Probability
Let estimator π(hat) = X(bar) for X1, X2, . . . , Xn, Xi ∼ Bernoulli(π)
Recall: P(X = x) = πx (1 − π)1−x , x ∈ {0, 1}
E(X) = π
V(X) = π(1 − π)
a. Show that π(hat) is a Consistent estimator of π
b. Find the Maximum Likelihood Estimator of π
c. Show that π(hat) is a Minimum Variance Unbiased Estimator of π
Please explain the answer in detail