Transcription of Chapter 3 Random Vectors and Multivariate Normal …
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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. WahedProperties of Mean and IfXandYare Random Vectors andA,B,CandDare constant matrices,thenE[AXB+CY+D]=AE[X]B+CE[Y]+D.
Random Vectors and Multivariate 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,
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