Hello :) Need help with the following question, and would appreciate if you could also explain the key steps

3. Suppose X = [X], . . . ,Xn] is a random sample from the distribution es} = (e 1)e2(1s}E2, rs: 2,3,... ; u e. e c. 1 The prior distribution for H is a beta distribution: I'(2n + 5} Tie} = F(4}I'(2n + 1} ramaw, uses] and the loss from estimating H by d is (5' (3)2. a} Find the posterior distribution of H conditional on K. 1:} Hence, calmlate the Bayes estimator ti of H. c} If the observations were 2,2,13,14,23 nd the estimate of 6' for this data. d} It was claimed that d is less than 0.4. Test the claim 1uia Bayesian testing with a zeroone loss, using the data from c}. Hint: You Ins].r nd it helpful to use the R function phets in your