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.

2. Let X1, ..., X6 be i.i.d from Pois(A) with _ _x; = 20. Suppose ) has the prior Gamma(a, B) with pdf Ba TT(X) : 10-1e-AB > >0; where a = 10, 3 = 4 T(a) (i) Find the Bayes Estimate of 1. (ii) Find a 90% credible interval for A (Use the x' table and equal tail areas) (iii) Test Ho : A = 3 vs H1 : A = 3.5 if they are the only possible values for A, with prior probabilities: 7(X = 3) = 2 and 7(X = 3.5) = 3