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.

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.

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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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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