65. Suppose that a random sample of size 20 is taken from a normal distribution with unknown mean and known variance equal to 1, and the mean is found to be x = 10, A normal distribution was used as the prior for the mean, and it was found that the posterior mean was 15 and the posterior standard deviation wa:s 0.1. What were the mean and standard deviation of the prior?

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65. Suppose that a random sample of size 20 is taken from a normal distribution
with unknown mean and known variance equal to 1, and the mean is found to
be x = 10, A normal distribution was used as the prior for the mean, and it was
found that the posterior mean was 15 and the posterior standard deviation wa:s
0.1. What were the mean and standard deviation of the prior?
Transcribed Image Text:65. Suppose that a random sample of size 20 is taken from a normal distribution with unknown mean and known variance equal to 1, and the mean is found to be x = 10, A normal distribution was used as the prior for the mean, and it was found that the posterior mean was 15 and the posterior standard deviation wa:s 0.1. What were the mean and standard deviation of the prior?
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