Answer Happy

a. We discussed in class today the multinomial probability distribution and its joint moment generating function. Here is a note on the multinomial distribution: A sequence of n independent experiments is performed and each experiment can result in one of r possible outcomes with probabilities p1.p2... Pr with pi = 1. Let X be the number of the n experiments that result in outcome i, i = 1,2,...,r. Then, P(X1 = T1, X2 = 22,...,X, = x) = nang PTp...p". The joint moment generating function of the multinomial distribution is given by My(t) = (pie't + pze"? + ... + prer)". Use properties of joint moment generating functions to find the probability distribution of X. b. Refer to question (a). Find the mean of X and the variance covariance matrix of X, where X = (X1, X2,...,xn).