. We have seen the Weibull distribution when discussing survival data analysis. Recall that Z ~ Weibull(a, A) if 2 has density fz(z) = 1le exp{-Az"}, z 2 0. (a) Find the survival function S (2) for Z and show that the Weibull satises the proportional hazards property with A = e". (b) Argue that 2 does not belong to the exponential family, but, for a known index a, Y = Z\" deal. In fact, what is the distribution of Y? ((2) Given data Z.- 5:3 Weibull(a,4\\.-), to: i = 1,...,n, with A.- = exp{a:'-T,6}, 1:.- the set of predictors for the i-th observation, derive the score estimating equation for a. Explain how you would obtain joint estimates for a and ,6 using the previous result about Yg