Suppose X₁,..., Xn when n > 2 are i.i.d Bernoulli(p) where 0 < p < 1 is unknown.(a) Find a sufficient statistic T(X₁,..., Xn) for p.(b) Show that 1 {X₁ = 1, X₂ = 0} is an unbiased estimator of p(1-p), where 1 {} denotesthe indicator function.(c) Use the Rao-Blackwell theorem to improve the above estimator.

It is given that X1, X2, ........, Xn follows Bernoulii distribution with parameter = p.

Answered: (a) Find a sufficient statistic…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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(a) Find a sufficient statistic T(X₁,..., Xn) for p. (b) Show that 1 {X₁ = 1, X₂ = 0} is an unbiased estimator of p(1-p), where 1 {} denotes the indicator function. (c) Use the Rao-Blackwell theorem to improve the above estimator.