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Chapter 4: Part b – The Multivariate Normal Distribution

Chapter 4: Part b – The Multivariate Normal Distribution. We will be discussing The Multivariate Normal Distribution Other Distributions (These topics are needed for Chapters 5). The Multivariate Normal Function.

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Chapter 4: Part b – The Multivariate Normal Distribution

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  1. Chapter 4: Part b – The Multivariate Normal Distribution • We will be discussing • The Multivariate Normal Distribution • Other Distributions • (These topics are needed for Chapters 5)

  2. The Multivariate Normal Function According to the multivariate density function, the probability that the random vector x = [x1 x2··· xp]′ takes on a particular set of values is given by The analogous distribution function is given by

  3. Bivariate Normal with Three Values of   = 0.0  = 0.4  = 0.6

  4. The 2 Distribution The Chi Square Is a Sum of Squared Z scores: Pr(2) It approaches normality as df gets large:

  5. Student’s t Distribution The t is analogous to the normal but with 2 unknown. It approaches normality also as the df gets large.

  6. The F Distribution The F is a ratio of Chi Squares. The t is an F2 with 1 df in the numerator.

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