Assessed at both Level 6 and 7: Assume that in an experiment data is drawn from the normal distribution N(,2). The prior for is N(,2). If x has been observed show that the posterior is proportional to N(21+212x+2,21+211) Moreover, if a random sample has been observed x1,x2,,xn (all iid with N(,2)), show that posterior given the sample mean X is N(2n+212nX+2,2n+211).

1. Assessed at both Level 6 and 7: Assume that in an experiment data is drawn from the normal
distribution N(,2). The prior for is N(,2). If x has been observed show that the posterior is
proportional to N(21+212x+2,21+211) Moreover, if a random sample has been observed x1,x2,,xn
(all iid with N(,2)), show that posterior given the sample mean X is N(2n+212nX+2,2n+211)