=+29.8. 1 Multinomial sampling. Let p ....., p, be positive and add to 1, and let Z1, Z2 ,... be independent k-dimensional random vectors such that Z ,, has with probability p, a 1 in the ith component and 0's elsewhere. Then f ,, =

(fm ,.... f.k) = Em _¡ Z ,, is the frequency count for a sample of size n from a multinomial population with cell probabilities p ;. Put Xni = (fn -np;)/ Vnp;

and X„ = (X ......., X ... ).