1. A random variable Y follows an inverse Gaussian distribution with parameters to > 0 and A > 0, denoted Y N |G(w, A), if it has density My): A) exP M , fory> 0. 21ry3 2w2y (a) Show that the inverse Gaussian distribution belongs to an exponential family. What are the canonical parameter 6, the cumulant b(6), and the dispersion 935? (b) Using the cumulant, nd the mean ,u and the variance of Y. What is the variance function V(,u)? (c) Obtain the canonical link for this distribution