Lecture 1. Random vectors and multivariate normal …
De nition 1. Let 2Rp and (p p) >0. A random vector X2R p has p-variate normal distribution with mean and covariance matrix if it has probability density function f(x) = j2ˇ 0j12 exp 1
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Random Variables and Probability Distributions
www.stat.pitt.eduCHAPTER 12 Random Variables and Probability Distributions Random Variables Suppose that to each point of a sample space we assign a number. We then have a function defined on the sam-
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www.stat.pitt.edun] is the p nmatrix of de-meaned random vectors. We claim the following: 1. Y j are normally distributed. 2. E(Y jY0 k) = ˆ; if j= k; 0; if j6=k. 3. P n i=1 Y iY 0= P n i=1 X~ i X~ i: 4. Y 1Y0 1 = n(X )(X )0: The facts 1 and 2 show the independence, while facts 3 and 4 give the distribution of S. Next lecture is on the inference about the ...
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