Suppose that a random sample of 100 observations is to be taken from a normal distribution for which the value of the mean is unknown and the standard deviation is 2, and the prior distribution of is a normal distribution Show that no matter how large the standard deviation of the prior distribution is, the standard deviation of the posterior distribution will be less than 1 5

Question: Suppose that a random sample of 100 observations is to be taken from a normal distribution for which the value of the mean is

Suppose that a random sample of 100 observations is to be taken from a normal distribution for which the value of the mean θ is unknown and the standard deviation is 2, and the prior distribution of θ is a normal distribution. Show that no matter how large the standard deviation of the prior distribution is, the standard deviation of the posterior distribution will be less than 1/5.

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