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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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