Let (X,..., Xn) be a random sample of binary random variables with P(X = 1) =...

 

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Let (X₁,..., Xn) be a random sample of binary random variables with P(X₁ = 1) = p = (0, 1). (i) Show that the sample mean X is an admissible estimator of p under the loss function (a - p)²/[p(1 - p)]. (ii) Show that X is an admissible estimator of p under the squared error loss. Let (X₁,..., Xn) be a random sample of binary random variables with P(X₁ = 1) = p = (0, 1). (i) Show that the sample mean X is an admissible estimator of p under the loss function (a - p)²/[p(1 - p)]. (ii) Show that X is an admissible estimator of p under the squared error loss.

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Solution i Let T m Consider the uniform distribu tin on the int... View the full answer