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Chapter 12 Multivariate normal distributions - Yale University

Page 1 Chapter 12 Multivariate normal distributionsThe Multivariate normal is the most useful, and most studied, of the standard joint dis-tributions in probability . A huge body of statistical theory depends on the properties of fam-ilies of random variables whose joint distribution is at least approximately Multivariate nor-mal. The bivariate case (two variables) is the easiest to understand, because it requires aminimum of notation; vector notation and matrix algebra becomes necessities when manyrandom variables are general bivariate normal is often used to model pairs of dependent random vari-ables, such as : the height and weight of an individual; or (as an approximation) the score astudent gets on a final exam and the total score she gets on the problem sets; or the heightsof father and son; and so on.

Page 1 Chapter 12 Multivariate normal distributions The multivariate normal is the most useful, and most studied, of the standard joint dis-tributions in probability.

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