Find the bayes estimate Suppose that X is a normal random va

Find the bayes estimate

Suppose that X is a normal random variable with unknown mean and known variance sigma^2=9 . The prior distribution for mu is normal with mu 0 = 4 and sigma^2 0= 1 . A random sample of n = 21 observations is taken, and the sample mean is X = 4.89 . Find the Bayes estimate of mu . mu is the expectation of X . Round your answer to three decimal places.

Solution

Baysean estimate for x bar = mu = 4.89