Correlation And Covariance Matrix For A Random Vector X We Define The Correlation Matrix Ry As X X X2 X X Ex Xx 1 (48.54 KiB) Viewed 34 times
Correlation And Covariance Matrix For A Random Vector X We Define The Correlation Matrix Ry As X X X2 X X Ex Xx 2 (48.54 KiB) Viewed 34 times
Correlation And Covariance Matrix For A Random Vector X We Define The Correlation Matrix Ry As X X X2 X X Ex Xx 3 (48.54 KiB) Viewed 34 times
Correlation and Covariance Matrix For a random vector X, we define the correlation matrix, Ry, as X X X2 ... X.X EX | XX, *² X2X, EX,X; Rx = E[XX")= E E[X;X] ... E[X1X,1] E[X3] ... E[XX,1 E[X,X,] E[X,X2] E[X1 ... XX X,X2 where shows matrix transposition. The covariance matrix, Cx, is defined as Cx = E[(X - EX)(X - EX)"] (X- EX;) (X2 - EX2)X1 – EXI) (X; - EX(X2 - EX) (X2 - EX2) (X1 - EX)(X, - EX) (X2 - EX2)(X, - EX = E (X, - Ex, (X, - EX,)(X1 - EX) (X, - EX, )(X2 - EX) Var(X) Cov(X1, X2) Cov(X1, X.) Cov(X2, X) Var(X2) Cov(X2, X.) II Cov(X), Xi) Cov(X,X2) Var(X.) The covariance matrix is a generalization of the variance of a random variable. Remember that for a random variable, we have Var(X) = EX2 - (EX). The following example extends this formula to random vectors.
Join a community of subject matter experts. Register for FREE to view solutions, replies, and use search function. Request answer by replying!