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Refer to question (a). Find the mean of X and the variance covariance matrix of X, where X = (X1, X2, ..., Xn)'.

Refer to question (a). Find the mean of X and the variance covariance matrix of X, where X = (X1, X2, ..., Xn)'.

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.3: Binomial Probability
Problem 2E: If a binomial experiment has probability p success, then the probability of failure is...
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Part B with hand written calculation and detailed explanations

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 = x1, X2 = x2,..., X, = n!nanulPï'p . p". The joint moment generating function of the multinomial distribution is given by Mx(t) = (Pie1 + pzet2 + probability distribution of X1. ... + pretr)". Use properties of joint moment generating functions to find the b. Refer to question (a). Find the mean of X and the variance covariance matrix of X, where X = : (X1, X2, ..., Xn)'.
Transcribed Image Text: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 = x1, X2 = x2,..., X, = n!nanulPï'p . p". The joint moment generating function of the multinomial distribution is given by Mx(t) = (Pie1 + pzet2 + probability distribution of X1. ... + pretr)". Use properties of joint moment generating functions to find the b. Refer to question (a). Find the mean of X and the variance covariance matrix of X, where X = : (X1, X2, ..., Xn)'.
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