2. Let X₁,..., Xn (n > 2) be a random sample from the Binomial (2,0) distribution, with probability mass function P(X₁ = k) = (2) 0¹ (1 - 0)²-k for k= 0, 1, 2. (a) Argue that Xi is a complete sufficient statistic for 0. (b) We are interested in estimating 04. By improving the estimator I(X₁ = 2, X₂ = 2) using the Rao-Blackwell theorem, find the best unbiased estimator of 04.
2. Let X₁,..., Xn (n > 2) be a random sample from the Binomial (2,0) distribution, with probability mass function P(X₁ = k) = (2) 0¹ (1 - 0)²-k for k= 0, 1, 2. (a) Argue that Xi is a complete sufficient statistic for 0. (b) We are interested in estimating 04. By improving the estimator I(X₁ = 2, X₂ = 2) using the Rao-Blackwell theorem, find the best unbiased estimator of 04.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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