Let (X1,..., Xn) be a random sample of binary random variables with P(X1 = 1) =...

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Let (X1,..., Xn) be a random sample of binary random variables with P(X1 = 1) = p E (0, 1). (i) Obtain the Bayes estimator of p(1 – p) when the prior is the beta dis- tribution with known parameter (a, B), under the squared error loss. (ii) Compare the Bayes estimator in (i) with the UMVUE of p(1 – p). (iii) Discuss the bias, consistency, and admissibility of the Bayes estimator in (i). (iv) Let [p(1 – p)]-I(0,1) (P) be an improper Lebesgue prior density for Show that the posterior of p given X;'s is a probability density provided that the sample mean X E (0, 1). (v) Under the squared error loss, find the generalized Bayes estimator of p(1 – p) under the improper prior in (iv). р. Let (X1,..., Xn) be a random sample of binary random variables with P(X1 = 1) = p E (0, 1). (i) Obtain the Bayes estimator of p(1 – p) when the prior is the beta dis- tribution with known parameter (a, B), under the squared error loss. (ii) Compare the Bayes estimator in (i) with the UMVUE of p(1 – p). (iii) Discuss the bias, consistency, and admissibility of the Bayes estimator in (i). (iv) Let [p(1 – p)]-I(0,1) (P) be an improper Lebesgue prior density for Show that the posterior of p given X;'s is a probability density provided that the sample mean X E (0, 1). (v) Under the squared error loss, find the generalized Bayes estimator of p(1 – p) under the improper prior in (iv). р.

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SoIuton Let i Since the postereior den fity geven Tt is proportion... View the full answer