Suppose that X is a normal random variable with unknown mean and known variance 2 9 The prior distribution for is normal with 0 4 and 2 0 1 A random sample of n 25 observations is taken, and the sample mean is x 4 85 (a) Find the Bayes estimate of (b) Compare the Bayes estimate with the maximum likelihood estimate

Question: Suppose that X is a normal random variable with unknown mean and known variance 2 = 9. The prior distribution for is normal

Suppose that X is a normal random variable with unknown mean and known variance σ₂ = 9. The prior distribution for μ is normal with μ₀ = 4 and σ²₀ = 1. A random sample of n = 25 observations is taken, and the sample mean is x = 4.85.

(a) Find the Bayes estimate of μ.

(b) Compare the Bayes estimate with the maximum likelihood estimate.

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