Exercise 15.7. *Using the general result that the conditional variance of a distribution in an exponential family is d2b(6) d62 V(Y) = 61(4)) and the values of a(-) and b(-) given in Table 15.9 (on page 444), verify that the variances of the Gaussian, binomial, Poisson, gamma, and inverse-Gaussian families are, consecutively, , M1 - 10/71, M, 45142, and W3- Table 15.9 Functions a(.), b(.), and c(.) for Constructing the Exponential Families Family a($ ) b(0 ) c( y, $ ) Gaussian 02 / 2 -ZLy2 / $ + loge (2TIQ) ] n Binomial loge(1 + e) loge ny Poisson -loge y! Gamma -loge (-0) p-'loge(y/4)-log ey-loger(4-1) Inverse-Gaussian -20 -2[loge (Itby3) + 1/ (by)]