Question: Consider the following model: x R N has a multivariate distribution with mean x and covariance x y R M has a multivariate distribution with

Consider the following model:

  • xRNhas a multivariate distribution with meanx and covariancex
  • yRMhas a multivariate distribution with meann and covariancen
  • y=Ax+b+nwhereARMN andbRM are constants
  1. Assume thatx andn are independent. Derive the mean and covariance of y.
  2. Assumex andn are not independent and have covariance:

Cov[x,n]=E[(xx)(nn)T]

Derive the mean and covariance ofy

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