LectureNotes12

LectureNotes12 - Multivariate Probability Distributions:...

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Unformatted text preview: Multivariate Probability Distributions: Part III Cyr Emile MLAN, Ph.D. mlan@stat.uconn.edu Multivariate Probability Distributions: Part III p. 1/1 Introduction Text Reference : Introduction to Probability and Its Applications, Chapter 6. Reading Assignment : Sections 6.6, April 20 We discuss now two special multivariate models: the multinomial distribution and the bivariate normal distribution . Multivariate Probability Distributions: Part III p. 2/1 Multinomial Distributions The multinomial distribution is an important generalization of the binomial distribution for situations where each of n independent trials can result in one of k distinct outcomes. Multinomial Experiment Definition 6.14 : A multinomial experiment possesses the following properties: The experiment consists of a fixed number n of identical trials. The outcome of each trial falls into one of k classes or cells . The probability that the outcome of a single trial will fall in a particular cell, say cell i , is p i , ( i = 1 , , k ) and remains the same from trial to trial. Note that p 1 + p 2 + + p k = 1 ....
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LectureNotes12 - Multivariate Probability Distributions:...

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