Can you please show all steps by hand and not using programs. I need help with seeing how this is done so I can properly study for my final exam. Thank you so much I will upvote if directions are followed.

1. Let X1, ..., X16 be i.i.d from N(u, o?) with o? = 16 given and ), T; = 128. (a) Use a Bayes Test to test Ho : A = 7 vs H1 : p = 9 if ? = {} consists of only these 2 points with prior probabilities: 7(/ = 7) = 3 and 7(/ = 9) = 1. (b) Suppose / can be any real value with a prior distribution (/) = N(6, 4). (i) Find the Bayes Estimate of p. (ii) Find the 95% Highest Posterior Density (HPD) credible interval for p. (iii) Use a Bayes Test to test Ho : / 9