Question (1) follows: Suppose that Xn form a random sample from a distribution for which the pdf f(x16) is as Oxe 1 for 0 < x < 1 f(x19) = o otherwise. Suppose also that the value of the parameter is unknown (9 > 0) and that the prior distribution of 9 is a gamma distribution with parameters a and (a > 0 and g > 0) as follows. f (xla,) = xa-le-x,x 0 rca) (a) Define the prior distribution of 0 with its support. (b) Define the likelihood function fn(X19). (c) Define the posterior distribution of 9, It(9 lx) with its support. (d) Determine the mean and the variance of the posterior distribution of 0 based on the squared error loss function.