Let v denote the volume of a three-dimensional figure. Let Y denote the number of
Chapter 6, Problem 6.115(choose chapter or problem)
Let v denote the volume of a three-dimensional figure. Let Y denote the number of particles observed in volume v and assume that Y has a Poisson distribution with mean v. The particles might represent pollution particles in air, bacteria in water, or stars in the heavens. a If a point is chosen at random within the volume v, show that the distance R to the nearest particle has the probability density function given by f (r) = 4r 2e(4/3)r3 , r > 0, 0, elsewhere. b If R is as in part (a), show that U = R3 has an exponential distribution.
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