please help me solve the problems below

A statistician wishes to find a Bayesian estimate of the mean of an exponential distribution with density function f(x)=-e""#. He is proposing to use a prior distribution of the form: prior (4) - "+T(a) You are given that the mean of this distribution is (-1 (i) Write down the likelihood function for / , based on a random sample of values 4,A, from an exponential distribution. [1] (ii) Find the form of the posterior distribution for /, and hence show that an expression for the Bayesian estimate for / under squared error loss is: D = [4] n+a-1 (iii) Show that the Bayesian estimate for / can be written in the form of a credibility estimate. and write down a formula for the credibility factor. (3] (iv) The statistician now decides that he will use a prior distribution of this form with parameters 0-40 and or-1.5. His sample data have statistics a -100, Ex; = 9,826, and Ex, =1,200,000. Find the posterior estimate for #, and the value of the credibility factor in this case. [3] Comment on the results obtained in part (iv). [Total 13]