M-dimensional gaussian random vector with expected value

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Reference no: EM131084503

Let X be a Gaussian (µ_X, C_X) random vector. Let Y = AX where A is an m ×n matrix of rank m. By Theorem 5.16, Y is a Gaussian random vector. Is a Gaussian random vector?

Theorem 5.16

Given an n-dimensional Gaussian random vector X with expected valueµ X and covariance CX, and an m × n matrix A with rank(A) = m,

Is an m-dimensional Gaussian random vector with expected value µ_Y = Aµ_X + b and covariance CY = AC_XA'

Reference no: EM131084503

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