Suppose that Yi' = 1,. . . ,n, are independent inverse gaussian random variables with unknown parameters [.51- and known parameter A. The probability density function of each K; is then given by: A f(y;u, A) = 2W3 exp { A(y #02} 2W2 u, A, y > 0 (a) Show that the distribution of Y;- is a member of the exponential family by identifying the canonical parameter, the dispersion parameter, and the functions a(>), (3(6), ((31; qb). (b) Obtain an expression for the mean and variance of 16;. (c) Identify the canonical link. (d) Suppose for each Y1- there is vector of explanatory variables xi- = (1133111- . .,m,;,p_1)'. Consider the linear predictor m- : xg/B', nd the specic form of the score vector and information matrix for E and explain how you would nd maximum likelihood estimates of g, l, . . . , 18304