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I'm trying to solve this exercise and I could use some help:

Suppose that the house of Lochness' monster, is found in a position X [expressed as km Est and km Nord from the city of Inverness] distributed as a Normal with mean $\mu$= (30; 50) and covariance structure $\Sigma$ = $\begin{matrix} 1 & 1 \\ 1 & 2 \\ \end{matrix}$.

find the mean squared distance from the city of Snakeburgh, located 31 km Est and 52 km Nord from Inverness.

My problem is that I only know the distribution of the Mahalanobis distance, but I need to compute the actual distance!

whuber
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mariob6
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    The distribution of the actual distance is obtained at http://stats.stackexchange.com/questions/9220 . That's a (very) hard way to go about solving this problem, though! Notice that you are asked for an expectation (the mean) of the squared distance. Why not calculate the expression of that squared distance? – whuber Jun 21 '16 at 14:11

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