(Solved): A 2-dimensional multivariate Gaussian probability density function \( g \) has mean vector \( m=\l ...

A 2-dimensional multivariate Gaussian probability density function \( g \) has mean vector \( m=\left[\begin{array}{l}2 \\ 2\end{array}\right] \) and covariance matrix \( C=\left[\begin{array}{cc}13 & -5.2 \\ -5.2 & 7\end{array}\right] \). The matrix \( C \) has eigenvalue decomposition \( C=U D U^{T} \), where: \[ U=\left[\begin{array}{cc} \cos \left(\frac{\pi}{3}\right) & -\sin \left(\frac{\pi}{3}\right) \\ \sin \left(\frac{\pi}{3}\right) & \cos \left(\frac{\pi}{3}\right) \end{array}\right], D=\left[\begin{array}{cc} 4 & 0 \\ 0 & 16 \end{array}\right] \] Carefully sketch a 1-standard-deviation contour for \( g \).