Suppose that XA has the Weibull survival function Sx^(x) = -, x 0, and A has an exponential distribution with mean 7. The Loglogistic distribution with parameters 7 and T2 has cdf F(x)= (x/T1) 1+ (x/7) 2 (a) Demonstrate that the marginal distribution of X is loglogistic, and express parameters for this loglogistic distribution in term of 7 and 0. (b) Write down the conditional expectation of X given A. (c) Given 0 = 1 and y = 2, using the conditional expectation to calculate E[X]. x 0. (For part (b) and (c), the following information might be helpful: For a Weibull r.v. with survival function S(x) = e-(x/a) for x > 0, we know it has mean a-I(1+1), where I'(y) is the complete gamma function T(y) = fot tu-edt, y > 0. The complete gamma function satisfies (y) (y- 1)(y-1), and in particular, l'(0.5)=.) =