. We have seen the Weibull distribution when discussing survival data analysis. Recall that Z ~ Weibull(a, A) if Z has density fz(z) = all?" exp{Az\"}, z 2 0. (:1) Find the survival function S (2) for Z and show that the Weibull 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 = 2'" does. In East, what is the distribution of Y? (0) Given data 2.; '5 Weibull(a,,\\.-), for z' = 1,I ...,n, with A.- = exp{z'-T}, z.- 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 13 using the previous result about K