(10 points) Show that the mean of the posterior distribution of M given in Theorem 10.6 can be written as 1=wx+(1w)0 that is, as a weighted mean of x and 0, where w=n+2/02nTheorem 10.6. If X is the mean of a random sample of size n from a normal population with the known variance 2 and the prior distribution of is a normal distribution with the mean 0 and the variance 02, then the posterior distribution of given X=x is a normal distribution with the mean 1 and the variance 12, where 1=n02+2nx02+02and121=2n+021.