Stats Solutions

(See Steps) You are given the random vector X^prime=[X_1, X_2, X_3, X_4] with mean vector \boldsymbolμ_X^prime=[3,2,-2,0] and variance-covariance matrix

Question: You are given the random vector \(\mathbf{X}^{\prime}=\left[X_{1}, X_{2}, X_{3}, X_{4}\right]\) with mean vector \(\boldsymbol{\mu}_{\mathbf{X}}^{\prime}=[3,2,-2,0]\) and variance-covariance matrix

\[\Sigma_{x}=\left[\begin{array}{llll} 3 & 0 & 0 & 0 \\ 0 & 3 & 0 & 0 \\ 0 & 0 & 3 & 0 \\ 0 & 0 & 0 & 3 \end{array}\right]\]

Let

\[A=\left[\begin{array}{rrrr} 1 & -1 & 0 & 0 \\ 1 & 1 & -2 & 0 \\ 1 & 1 & 1 & -3 \end{array}\right]\]
  1. Find \(E(\mathbf{A X})\), the mean of \(\mathbf{A X}\).
  2. Find \(\operatorname{Cov}(\mathbf{A X})\), the variances and covariances of \(\mathbf{A X}\).
  3. Which pairs of linear combinations have zero covariances?

Price: $2.99
Solution: The downloadable solution consists of 1 pages
Deliverable: Word Document


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