# Question

A vector random variable, X, has a mean vector and correlation matrix given by

A new random vector is formed according to where the matrix is given by

Find the mean vector, correlation matrix and covariance matrix of Y.

A new random vector is formed according to where the matrix is given by

Find the mean vector, correlation matrix and covariance matrix of Y.

## Answer to relevant Questions

A vector random variable, X has a covariance matrix and a correlation matrix given by Find the mean vector, E [X]. For any four zero- mean Gaussian random variables X1, X2, X3, and X4, show that . E [X1X2X3X4] = E [X1X2] E[X3X4] + E [X1X3] E [X2X4] + E [X1X4] E [X2X3] You might want to use the result of the previous exercise. Note: This ...Suppose, X, Y, and Z are independent, zero- mean, unit- variance Gaussian random variables. (a) Using the techniques outlined in Section 6.4.2, find the characteristic function of W = XY + XZ + YZ. (b) From the ...Let be the random vector described. (a) Find the LMMSE estimator of given observation of {X2= x2, X3= x3}. (b) Find the MSE of the estimator in part (a). (c) Explain why we cannot find the MAP or ML estimators in this ...Suppose a point in three- dimensional Cartesian space, (X, Y, Z) is equally likely to fall anywhere on the surface of the hemisphere defined by X2 + Y2 + Z2 = 1 and Z ≥ 0. (a) Find the PDF of Z, fZ (z). (b) Find the ...Post your question

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