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Homework : 2 Q₁ Let = (0, 1) and Q[0, 1]. Let L(0, a) = (a-0)2 and let X ~ B(n,0). Let the prioir distrin is O~ Beta(a, b) = T(a + 3) ga-1 (1-0)³-1, 0 € (0, 1), a > 0, 3 >0. г(a)(3) 1. Show that the Bayes rule is a+x d(x) = a+ẞ+n 2. Show that the maximum likelihood estimate of 0 d₁(x): rule. = x/n, is not a Bayes 3. Show that d₁(x) is a limit of Bayes rules. 4. Show that d₁(x) is generalized Bayes with respect to 0 = 7 = π(0) = 1/(0(1 − 0)). 5. Show that d₁(x) is extended Bayes.

Homework : 2 Q₁ Let = (0, 1) and Q[0, 1]. Let L(0, a) = (a-0)2 and let X ~ B(n,0). Let the prioir distrin is O~ Beta(a, b) = T(a + 3) ga-1 (1-0)³-1, 0 € (0, 1), a > 0, 3 >0. г(a)(3) 1. Show that the Bayes rule is a+x d(x) = a+ẞ+n 2. Show that the maximum likelihood estimate of 0 d₁(x): rule. = x/n, is not a Bayes 3. Show that d₁(x) is a limit of Bayes rules. 4. Show that d₁(x) is generalized Bayes with respect to 0 = 7 = π(0) = 1/(0(1 − 0)). 5. Show that d₁(x) is extended Bayes.

MATLAB: An Introduction with Applications
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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Statistical Decision Theory
Homework : 2 Q₁ Let = (0, 1) and Q[0, 1]. Let L(0, a) = (a-0)2 and let X ~ B(n,0). Let the prioir distrin is O~ Beta(a, b) = T(a + 3) ga-1 (1-0)³-1, 0 € (0, 1), a > 0, 3 >0. г(a)(3) 1. Show that the Bayes rule is a+x d(x) = a+ẞ+n 2. Show that the maximum likelihood estimate of 0 d₁(x): rule. = x/n, is not a Bayes 3. Show that d₁(x) is a limit of Bayes rules. 4. Show that d₁(x) is generalized Bayes with respect to 0 = 7 = π(0) = 1/(0(1 − 0)). 5. Show that d₁(x) is extended Bayes.
Transcribed Image Text:Homework : 2 Q₁ Let = (0, 1) and Q[0, 1]. Let L(0, a) = (a-0)2 and let X ~ B(n,0). Let the prioir distrin is O~ Beta(a, b) = T(a + 3) ga-1 (1-0)³-1, 0 € (0, 1), a > 0, 3 >0. г(a)(3) 1. Show that the Bayes rule is a+x d(x) = a+ẞ+n 2. Show that the maximum likelihood estimate of 0 d₁(x): rule. = x/n, is not a Bayes 3. Show that d₁(x) is a limit of Bayes rules. 4. Show that d₁(x) is generalized Bayes with respect to 0 = 7 = π(0) = 1/(0(1 − 0)). 5. Show that d₁(x) is extended Bayes.
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