Suppose that Y i is Poisson with g( i ) = a + x i , where

Suppose that Y_i is Poisson with g(µ_i) = a + βx_i, where x_i = 1 for i = 1,..., n_A from group A and x_i = 0 for i = n_A + 1,..., n_A + n_B from group B. Show that for any link function g, the likelihood equations (4.22) imply that fitted means µ̂_A and µ̂_B equal the sample means.