Let X1, X2,..., XniidBernoulli(p).(a) Find a one-dimensional sufficient statistic S for the Bernoulli distribution.(b) Find E[X(1-X1)] and then find an unbiased estimator of r(p) = p(1- p) based on theexpression in the expectation.(c) Find E[I{x;=1}l.(d) Find E[I{x,=1}|S].

Given X1, X2, ..., Xn~iidBernoullip

Answered: Let X1, X2,..., Xn " Bernoulli(p). (a)…

A First Course in Probability (10th Edition)

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Chapter1: Combinatorial Analysis

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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Let X1, X2,..., Xn " Bernoulli(p). (a) Find a one-dimensional sufficient statistic S for the Bernoulli distribution. (b) Find E[X(1–X1)] and then find an unbiased estimator of r(p) = p(1 – p) based on the expression in the expectation. (c) Find E[I{x1=1}]- (d) Find E[I{x1=1}|S].