The Diastolic Blood Pressure is measured for a random sample of 10 persons and reported below: 62 63 64 67 70 72 76 77 81 81 Assuming the Diastolic Blood Pressure follows normal distribution and the variance is known to be 52, answer the following questions:

. What is the conjugate family of prior distributions for a normal mean1 p, when the variance, 02, is known? . Assume that the value of variance 02 = 52. and a researcher used 05 = 0.35. What is sample size equivalent to the information in this prior? . What is the posterior distribution p(u| y) under prior distribution N010 = 70, 03 = 100)? . Find the posterior mean, median1 mode, and posterior variance of p using the posterior distribution you calculated in (c)