(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.
(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.
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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![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 {} denotes
the indicator function.
(c) Use the Rao-Blackwell theorem to improve the above estimator.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7b7a7eaa-ccf3-40e1-875c-26f3d1076957%2F800c9924-f4f8-48ba-a9be-3fb9246a705a%2Fpu1bkj8_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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 {} denotes
the indicator function.
(c) Use the Rao-Blackwell theorem to improve the above estimator.
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