I'm learning about the Mahalanobis Distance, and I had a question regarding an interesting problem:
Let $x = \begin{bmatrix} x_1 \\ x_2 \end{bmatrix}$ be a Gaussian random vector with mean $\mu = \begin{bmatrix} \mu_1 \\ \mu_2 \end{bmatrix}$ and covariance $P = \sigma^2 I$. Let $y = \begin{bmatrix} y_1 \\ y_2 \end{bmatrix}$. What is the Mahalanobis Distance (MD) of $y$ relative to the distribution of $x$?
There are a few questions on StackExchange about the Mahalanobis Distance (such as: How to calculate the Mahalanobis distance), but I'm not sure I quite understand how to apply it in this circumstance at an abstract level. Furthermore, is the problem suggesting that the Mahalanobis distance is affected by the Probability Density function? Would anyone be able to assist me in solving this? Thanks for your time and help in advanced!