Transcription of Chapter 3 Random Vectors and Multivariate Normal …
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Chapter 3 Random Vectors and Multivariate Normal …
Chapter 3 Random Vectors and MultivariateNormal Random vectorsDefinition Random Vectors are Vectors of random83 BIOS 2083 Linear ModelsAbdus S. Wahedvariables. For instance,X= ,where each element represent a Random variable, is a Random Mean and covariance matrix of a Random mean (expectation) and covariance matrix of a Random vectorXis de-fined as follows:E[X]= E[X1]E[X2]..E[Xn] ,andcov(X)=E {X E(X)}{X E(X)}T = 21 1n 21 n1 2n ,( )where 2j=var(Xj)and jk=cov(Xj,Xk)forj, k=1,2,.., 384 BIOS 2083 Linear ModelsAbdus S.
Normal Distributions 3.1 Random vectors Definition 3.1.1. Random vector. Random vectors are vectors of random 83. BIOS 2083 Linear Models Abdus S. Wahed variables. For instance, X= ... T is said to follow a multivariate normal distribution
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