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)...

See the question below and please respond to parts a through m:

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 thto answer questions (e ) and (d) below. All other parts of this questions can be attempted this week(i) Show that, for 0 < a < 1, the (100a)th percentile, na , of the posterior density is given byAnswer the following by first principles. Hint: You may need to wait till after Lecture on March 12(f) State the support, Sply , the normalizing constant and the kernel, of the posterior density.(g) Show that E |: |y =t - () . Give a verbal interpretation of your answer. Hint: Use(m) Is the statistic W = 27 + 1 sufficient for 8, where T = min{Yi , Ya,., Ya)? Explain.Let Y = Y1, Yz..., Ya 1 8 be ii.d with a common sampling model, given by p2(y | 8).(1) Compute P(8 :$ 4.8| t'). Give a verbal interpretation of your answer.(h) For any number a S t, show that P[o < < | y] = e"(a-o(e) Show that the posterior density is a proper distribution.central 95% posterior credible interval for B.(b) State the support, Sa , of the prior density.(c) Show that T is a sufficient statistic for 8.integration-by-parts from Calculus.(a) Show that the prior is improper.2. Consider the Bayesian model given byT = t, is given by(k) Write down p4 (8 | t')Let T = min{Yi , Yz . .up Ya].