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

Let estimator π(hat) = X(bar) for X1, X2, . . . , X_n, X_i ∼ Bernoulli(π)

Recall: P(X = x) = π^x (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

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orchestra answered 1 year ago

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