Math Solutions

[Solution Library] You are given the random vector X^prime=[X_1, X_2, ..., X_5] with mean vector μ_x^prime=[2,4,-1,3,0] and variance-covariance matrix

Question: You are given the random vector \(\mathbf{X}^{\prime}=\left[X_{1}, X_{2}, \ldots, X_{5}\right]\) with mean vector \(\mu_{\mathbf{x}}^{\prime}=[2,4,-1,3,0]\) and variance-covariance matrix

\[\boldsymbol{\Sigma}_{\mathbf{X}}=\left[\begin{array}{rrrrr} 4 & -1 & \frac{1}{2} & -\frac{1}{2} & 0 \\ -1 & 3 & 1 & -1 & 0 \\ \frac{1}{2} & 1 & 6 & 1 & -1 \\ -\frac{1}{2} & -1 & 1 & 4 & 0 \\ 0 & 0 & -1 & 0 & 2 \end{array}\right]\]

Partition \(\mathbf{X}\) as

\[\mathbf{x}=\left[ \begin{matrix} {{X}_{1}} \\ {{X}_{2}} \\ {{X}_{3}} \\ {{X}_{4}} \\ {{X}_{5}} \\ \end{matrix} \right]=\left[ \frac{{{\mathbf{X}}^{(1)}}}{{{\mathbf{X}}^{(2)}}} \right]\]

Let

\[\mathbf{A}=\left[\begin{array}{rr} 1 & -1 \\ 1 & 1 \end{array}\right] \text { and } \quad \mathbf{B}=\left[\begin{array}{rrr} 1 & 1 & 1 \\ 1 & 1 & -2 \end{array}\right]\]

and consider the linear combinations \(\mathbf{A} \mathbf{X}^{(1)}\) and \(\mathbf{B X}^{(2)}\). Find

  1. \(E\left(\mathbf{X}^{(1)}\right)\)
    (f) \(E\left(\mathbf{B} \mathbf{X}^{(2)}\right)\)
    (j) \(\operatorname{Cov}\left(\mathbf{A} \mathbf{X}^{(1)}, \mathbf{B X}^{(2)}\right)\)
    Price: $2.99
    Solution: The downloadable solution consists of 2 pages
    Deliverable: Word Document


    ∴ Other downloads you may be interested in ∴

log in to your account

Forgot password?
Don't have a membership account?
REGISTER

reset password

Back to
log in

sign up

Back to
log in