Let $n$ point are distributed as per a homogeneous spatial Poisson process of rate $λ$ in a square of side $2a$, and assume that $4$ fixed points are located at $(a/2,a/2)$, $(-a/2,a/2)$, $(a/2,-a/2)$ and $(-a/2,-a/2)$, when the center of the square is $(0,0)$. If the sum of the distance between each random point and 4 fixed points be a random variable called X. How can I find the expected value $E(X)$?

  • $\begingroup$ What makes you think this has an answer? Closed forms of mean Euclidean distances (as opposed to mean squared Euclidean distances) are notoriously difficult/impossible to compute. $\endgroup$ – Did Jan 31 at 9:15
  • $\begingroup$ The expected value of the distance between the random points and the center of the square is computed in link. $\endgroup$ – S Doostali Feb 2 at 6:54

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