Question: 5.5.4 Consider spheres in three-dimensional space with centers distributed according to a Poisson distribution with parameter jAj, where jAj now represents the volume of the

5.5.4 Consider spheres in three-dimensional space with centers distributed according to a Poisson distribution with parameter jAj, where jAj now represents the volume of the set A. If the radii of all spheres are distributed according to F.r/

with density f .r/ and finite third moment, show that the number of spheres that cover a point t is a Poisson random variable with parameter 43

R1 0 r3f .r/dr.

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