Please help with part c and how to determine how T is a sufficient statistic; part g in how to use integration by parts to show that the posterior density is as shown in part g (correct posterior is in part d); and help with part h in what to use to come up with the derivation.

P1(8) = 11(-so,ce ) (B) Pz(y | 8) = e-(-8) [(8,ce) (v) variance, and an equal-tail 99% probability interval, of the posterior distribution of Ta- (d) Show that the posterior density of 0, conditional on Y = y = (y1. yz..., yn), or equivalently ()Assume now that, based on the data at the end of the experiment, n = 10, t' = 5. Compute th to answer questions (e ) and (d) below. All other parts of this questions can be attempted this week (i) Show that, for 0