Q1: Let = (0, 1) and Q = [0, 1]. Let L(0, a) = (a)2 and let X ~ B(n, 0). Let the prioir distrin is Ꮎ ~ Beta(a, b) = г (a + B) pa−1 (1 - 0) ³-1, 0 € (0, 1), a > 0, ẞ > 0. г(a)г(B) 1. Show that the Bayes rule is α + x d(x) = = a + B + n 2. Show that the maximum likelihood estimate of 0 d₁(x) = x/n, is not a Bayes rule. 3. Show that d₁(x) is a limit of Bayes rules. π(0) = 1/(0(1 − 0)). 4. Show that d₁(x) is generalized Bayes with respect to 0 = π 5. Show that d₁(x) is extended Bayes.

Q1: Let = (0, 1) and Q = [0, 1]. Let L(0, a) = (a)2 and let X ~ B(n, 0). Let the prioir distrin is Ꮎ ~ Beta(a, b) = г (a + B) pa−1 (1 - 0) ³-1, 0 € (0, 1), a > 0, ẞ > 0. г(a)г(B) 1. Show that the Bayes rule is α + x d(x) = = a + B + n 2. Show that the maximum likelihood estimate of 0 d₁(x) = x/n, is not a Bayes rule. 3. Show that d₁(x) is a limit of Bayes rules. π(0) = 1/(0(1 − 0)). 4. Show that d₁(x) is generalized Bayes with respect to 0 = π 5. Show that d₁(x) is extended Bayes.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.6: Additional Trigonometric Graphs

Problem 78E

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