1. The Pareto distribution is a continuous power law distribution widely used to describe many datasets in social sciences and economics. If Z ~ Pareto(po, a) then P(Z > z) = 2 2 /01 where u is the minimum value for Z, assumed known, and o is the Pareto inder. (a) Find the density of Z and then argue that Z does not belong to the exponential family. (b) While Z does not belong to the exponential family, Y - log Z does. What are the canonical parameter and the cumulant function for Y? (c) Using the cumulant, find the mean / and the variance of Y. What is the variance function V()? Now obtain the canonical link for the distribution of Y. (d) Show that Y -log / ~ Exponential(a). How would you regress Z on a set of predictors X to estimate the Pareto index using glm