Suppose that a random sample X1, . . . ,Xn is to be taken from the normal distribution with unknown mean and variance 100,

Suppose that a random sample X1, . . . ,Xn is to be taken from the normal distribution with unknown mean θ and variance 100, and the prior distribution of θ is the normal distribution with specified mean μ0 and variance 25. Suppose that θ is to be estimated using the squared error loss function, and the sampling cost of each observation is 0.25 (in appropriate units). If the total cost of the estimation procedure is equal to the expected loss of the Bayes estimator plus the sampling cost (0.25)n, what is the sample size n for which the total cost will be a minimum?