. We have seen the Weibull distribution when discussing survival data analysis. Recall that Z ~ Weibull(a, A) if Z has density [2(2) = aAz'lexp{Az}. z 2 0. (11.) Find the survival function S (2) for Z and show that the Weihull satises the proportional hazards property with A = e". (b) Argue that Z does not belong to the exponential family. but. for a known index a, Y = Z\" does. In fact, what is the distribution of Y? ((3) Given data 2.1 '33 Weibull(a,A.-), for 1' = 1,...,n, with A.- = exp{s:T}, 3.1 the set of predictors for the i-th observation, derive the score estimating equation for (1. Explain how you would obtain joint estimates for a and ,6 using the previous result about Yi