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In 2D or 3D I have a fix point y and Gaussian distribution of a random point x. I am now interested in the mean euclidean distance between x and y:

$E_x [ d(x,y) ] = \int _{-\infty }^{\infty } d(x,y) N(x; \mu, \Lambda )dx$

Many thanks in advance

  • 1
    In 2D, if the components of $X$ are independent normal variables with the same variance, then look at http://en.wikipedia.org/wiki/Rice_distribution. Note the formula for the mean, and the first item in the section "Related distributions".2011-01-24

3 Answers 3