4.5 The Multinomial, the Bivariate Normal, and the Multivariate Normal Distributions

In this section, we introduce and study to some extent three multidimensional distributions; they are the Multinomial distribution, the two-dimensional Normal or Bivariate Normal distribution, and the k-dimensional Normal distribution.

4.5.1 Multinomial Distribution

A Multinomial experiment is a straightforward generalization of a Binomial experiment, where, instead of 2, there are k (mutually exclusive) possible outcomes, O1,…, Ok, say, occurring with respective probabilities p1,…,pk. Simple examples of Multinomial experiments are those of rolling a die (with 6 possible outcomes); selecting (with replacement) r balls from a collection of n1 +···+ nk balls, ...

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