1. Show that the following distributions belong to the exponential family. Find the natural parameter 0, scale parameter o and convex function b(0). Also find the EY and Var(Y) as functions of the natural parameter. Specify the canonical link functions. (a) Exponential distribution Exp()), f(y; )) = de-dy; (b) Binomial distribution Bin(n, T), f(y; 7) = (")Ty(1 -4)"-3, where n is known; (c) Poisson distribution Pois()), f(y; )) = 4xye-1; (d) Chi-squared distribution X(k), f(y; k) = 1 k T(k),yz e ? (no need to specify the canonical link function); (e) Negative binomial distribution NB(m, B), f(y; B) = (3+m- 1) (m(1 -3)3, where m is known; (f) The Gamma distribution Gamma(a, B), f(y; B) = Ba roya le By, where the shape parameter o is known