CSCC37H3 Lecture Notes - Multivariate Normal Distribution, Absolute Continuity, Marginal Distribution
27 Jun 2013
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3. 5 multivariate normal distribution: de ntion: a random vector (x1, x2, . 2 n if it has joint probability density function given by fx1,,xn(x1, . 2 ( x )t 1( x )} for (x1, . , xn) rn and we write (x1, x2, . , xn)t nn( , : again is a location parameter and is a spread parameter this time in rn, is symmetric. For example ij = ji: we"ll assume throughout that is positive de nite. Y (( we will often write = xy. Denote by (x, y )t the random vector where x is the weight of a b52 student in pounds and y equals the height of the same b52 student in feet. Suppose that (x, y )t n2"" x. A well known result in linear algebra implies. 49 ( x )t 1( x ) = (x x, y y ) Y (x x)2 2 x y (x x)(y y ) + 2.
