3. A person believes that his last year's weight was normally distributed with mean of 165 lb and standard deviation of
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3. A person believes that his last year's weight was normally distributed with mean of 165 lb and standard deviation of 5 bl. That is, the prior pdf of μ~ N(165,25). He expects his current weight X is normally distributed with mean μ and standard deviation 7 lb. Following are 10 random measurements from this year a) Compute the Posterior mean μ₁ and Posterior variance of by using the result of example 1 from lecture 3, which can be simplify as (or = H₁ = 12 176 165 180 172 175 179 166 177 184 183 %0 x+²) and ² = (or = no²+0² b) A 95% credible interval for the mean u. x-mean [Hints: 1 - a = 0.95, Zx standard deviation , choose a = -b] c) Test the hypothesis Ho: ≤170 vs. H₁: μ> 170. o²a no+0². (4 marks) (7 marks) (10 marks)