40. In the situation of Example 7, consider the following model in which the row margins are fixed and which therefore generalizes model (iii) of Chapter 4, Section 7. A sample of n ; subjects is obtained from class Ai (i = 1, . . . , a), the samples from different classes being independent. If nij is the number of subjects from the i th sample belonging to Bj (j = 1, .. . , b), the joint distribution of (nil, . . . , nih) is multinomial, say, M(n i; Plli" ",Phl;)' Determine the likelihood-ratio statistic for testing the hypothesis of homogeneity that the vector (Pili" . . , Phi;) is independent of i , and specify its asymptotic distribution.