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Let XI, , Xk be multinomial MN(n,Pi P2, • • . ,Pk) with EXi = 71)E n = 1. For k = 2 , nn,12 derive the asymptotic distribution of Q = E k oc= npir” . i=i
Explanations are in the attached file.
Web page http://en.wikipedia.org/wiki/Multinomial_distribution contains definition of multinomial distribution. For k = 2 it is the same as the binomial distribution whose properties can be found on web page http://en.wikipedia.org/wiki/Binomial_distribution. Taking notations X=X_1 and p=p_1, we have, for k=2,
X_2=n-X, p_2=1-p. …
This solution encompasses asymptotic distribution.