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  3. let estimator π(hat) = x(bar) for x1, x2, . .

Let estimator π(hat) = X(bar) for X1, X2, . . . , Xn, Xi ∼ Bernoulli(π) Recall:...

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Statistics

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 ofπ

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