Suppose that X is a normal random variable with unknown  mean μ and known variance σ2 . The prior distribution for μ is a  uniform distribution defined over the interval [a b, ]. (a) Find the posterior distribution for μ. (b) Find the Bayes estimator for μ.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
Question

Suppose that X is a normal random variable with unknown 
mean μ and known variance σ2
. The prior distribution for μ is a 
uniform distribution defined over the interval [a b, ].
(a) Find the posterior distribution for μ.
(b) Find the Bayes estimator for μ.

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