*9.65In this exercise, we illustrate the direct use of the Rao-Blackwell theorem. Let Y₁, Y₂,..., Ybe independent Bernoulli random variables withp(y;|p) = p (1-p)¹-*, y = 0, 1.That is, P (Y; = 1) = p and P(Y; = 0) = 1 - p. Find the MVUE of p(1 - p), which is aterm in the variance of Y, or W=Y₁, by the following steps.a LetShow that E(T) = p(1 - p).b Show thatсT =Show that1, if Y₁ = 1 and Y₂ = 0,0, otherwise.P(T=1| Ww) =-w (n − w)n(n-1)nE(T | W) = ²₁ [ (¹-W)] = ²¹--Y(1-Y)nn-1and hence that nỸ(1-Y)/(n-1) is the MVUE of p(1 - p).

Answered: Image /qna-images/answer/594fa410-7881-4ebc-92e2-9c0298072976.jpg

Answered: p(y|p) = p (1-p)¹-5, y = 0, 1. hat is,…

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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p(y|p) = p (1-p)¹-5, y = 0, 1. hat is, P(Y; = 1) = p and P(Y; = 0) = 1 - p. Find the MVUE of p(1 - p), rm in the variance of Y, or W = Y, by the following steps. Let T = Show that E(T) = p(1-P). Show that Show that 1, if Y₁ = 1 and Y₂ = 0, 0, otherwise. P(T=1| Ww) = w (n − w) n(n − 1) B.