# expected value from some points in continuous homogeneous spatial Poisson point process

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 $$E(X)$$?

• 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. – Did Jan 31 at 9:15
• The expected value of the distance between the random points and the center of the square is computed in link. – S Doostali Feb 2 at 6:54