$X$ and $Y$ are jointly Gaussian random variables with zero mean.
A constant-pdf contour is where the joint density function takes on the same value. If the constant-pdf contours of $X, Y$ are as shown above, which of the following could their covariance matrix $\mathbf{K}$ be:
- $\mathbf{K}=\left[\begin{array}{cc}1 & 0.5 \\ 0.5 & 1\end{array}\right]$
- $\mathbf{K}=\left[\begin{array}{cc}1 & -0.5 \\ -0.5 & 1\end{array}\right]$
- $\mathbf{K}=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$
- $\mathbf{K}=\left[\begin{array}{ll}1 & 0 \\ 0 & 2\end{array}\right]$
- $\mathbf{K}=\left[\begin{array}{cc}1 & -0.5 \\ -0.5 & 2\end{array}\right]$