Given the problem below, find the posterior distribution of .

Let 0 be the true I.Q. of a certain student. To measure his I.Q., the student takes an I.Q. test. Students' I.Q. test score, X, follows a normal distribution with mean 0 and variance 25. Suppose that the true I.Q.'s of students vary according to income groups and that they are distributed normally with mean 100 and variance 225. If the random sample consists of one observation X = 120, a. find the posterior distribution of e Hint: In solving for the integral part, try to reduce it into an integral of some known probability distribution so that it will simplify or converge to unity