Homework : Q1: Let e == (0, 1) and Q = [0,1]. Let L(0, a) = (a - 0) 2 and let X 2 B(n,0). Let the prioir distrin is ~Beta(a, 3) = T(a+B) г(a)г(3) 0-1 (1-0)-1, 0 (0, 1), a > 0, 3>0. 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) = x/n, is not a Bayes rule. 3. Show that d₁(x) is a limit of Bayes rules. 4. Show that d₁(x) is generalized Bayes with respect to 0 = (0) = 1/(0(1 - 0)). 5. Show that d₁(x) is extended Bayes.
Homework : Q1: Let e == (0, 1) and Q = [0,1]. Let L(0, a) = (a - 0) 2 and let X 2 B(n,0). Let the prioir distrin is ~Beta(a, 3) = T(a+B) г(a)г(3) 0-1 (1-0)-1, 0 (0, 1), a > 0, 3>0. 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) = x/n, is not a Bayes rule. 3. Show that d₁(x) is a limit of Bayes rules. 4. Show that d₁(x) is generalized Bayes with respect to 0 = (0) = 1/(0(1 - 0)). 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 77E
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Question
![Homework :
Q1: Let e
==
(0, 1) and Q = [0,1]. Let L(0, a) = (a - 0) 2 and let X
2
B(n,0). Let the
prioir distrin is
~Beta(a, 3) =
T(a+B)
г(a)г(3)
0-1 (1-0)-1, 0 (0, 1), a > 0, 3>0.
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) = x/n, is not a Bayes
rule.
3. Show that d₁(x) is a limit of Bayes rules.
4. Show that d₁(x) is generalized Bayes with respect to 0 = (0) = 1/(0(1 - 0)).
5. Show that d₁(x) is extended Bayes.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa616cd7b-6ecd-4e0f-b539-532f33c9abef%2Fbbbda8bc-a66a-4c79-9f98-f5a3379fbbf2%2Fo16d79_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Homework :
Q1: Let e
==
(0, 1) and Q = [0,1]. Let L(0, a) = (a - 0) 2 and let X
2
B(n,0). Let the
prioir distrin is
~Beta(a, 3) =
T(a+B)
г(a)г(3)
0-1 (1-0)-1, 0 (0, 1), a > 0, 3>0.
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) = x/n, is not a Bayes
rule.
3. Show that d₁(x) is a limit of Bayes rules.
4. Show that d₁(x) is generalized Bayes with respect to 0 = (0) = 1/(0(1 - 0)).
5. Show that d₁(x) is extended Bayes.
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