Question

zero mean gaussian random variables x1,x2 and x3 having a covariance matrix.
c(x)={4 2.05 1.05} {2.05 4 2.05} {1.05 2.05 4}. Find the covariance matrix

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5. zero-mean gaussian random variables x1, x2, and x3 having a covariance matrix 4 2.05 1.05 [cx) = 2.05 4 2.05 1.05 2.05 4 are transformed to new variables y1 = 5x1 + 2x2 - x3 y2 = -x1 +3x2 + x3 y3 = 2x1 - x2 + 2x3 (a) find the covariance matrix of yı, y2, and y3. (b) write an expression for the joint density function of yı, y2, and y3. don't write it out

Question: 5. Zero-Mean Gaussian Random Variables X1, X2, And X3 Having A Covariance Matrix 4 2.05 1.05 [Cx) = 2.05 4 2.05 1.05 2.05 4 Are Transformed To New Variables Y1 = 5X1 + 2X2 - X3 Y2 = -X1 +3X2 + X3 Y3 = 2X1 - X2 + 2X3 (A) Find The Covariance Matrix Of Yı, Y2, And Y3. (B) Write An Expression For The Joint Density Function Of Yı, Y2, And Y3. Don't Write It Out

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Transcribed image text: 5. Zero-mean Gaussian random variables X1, X2, and X3 having a covariance matrix 4 2.05 1.05 [Cx) = 2.05 4 2.05 1.05 2.05 4 are transformed to new variables Y1 = 5X1 + 2X2 - X3 Y2 = -X1 +3X2 + X3 Y3 = 2X1 - X2 + 2X3 (a) Find the covariance matrix of Yı, Y2, and Y3. (b) Write an expression for the joint density function of Yı, Y2, and Y3. Don't write it out in full, just give the general form, then explicitly provide the mean vector and covariance matrix. (c) A MATLAB function can be used to solve the last problem given earlier. The calling syntax can be function (my, Kyy] = covprop(mx, Kxx, A). It can compute the mean and covariance output, given the input to a linear system described by a matrix A, as discussed in class.