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Chapter 3 Random Vectors and Multivariate Normal …

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Chapter 3Random Vectors and MultivariateNormal Random vectorsDefinition Random Vectors are Vectors of random83BIOS 2083Linear 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,..., 384BIOS 2083Linear ModelsAbdus S. WahedProperties of Mean and IfXandYare Random Vectors andA,B,CandDare constant matrices,thenE[AXB+CY+D]=AE[X]B+CE[Y]+D. ( ) as an For any Random vectorX, the covariance matrixcov(X) is as an IfXj,j=1,2.

Chapter 3 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, ... Marginal and Conditional distributions Suppose X is N n(μ,Σ) ...

  Chapter, Distribution, Normal, Vector, Chapter 3, Multivariate, Vectors and multivariate normal, Vectors and multivariate normal distributions 3

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