For the multinomial distribution with p = rank( i,j) = k 1, show that and hence

For the multinomial distribution with p = rank(κ

i,j) = k − 1, show that and hence that

ρ4 = ρ

2 13 − 2/m = ρ

2 23 − k/m, showing that the inequalities in Exercises 2.12 and 2.14 are sharp for m = 1. Show also that the minimum value of ρ

2 13 for the multinomial distribution is (k − 2)/m.