Suppose that X is a normal random variable with unknown mean and known variance 2 The prior distribution for is a uniform distribution defined over the interval a, b (a) Find the posterior distribution for (b) Find the Bayes estimator for ...

a the joint distribution is and this integral ...

Suppose that X is a normal random variable with unknown mean and known variance 2

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.

Distribution
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