Let v denote the volume of a three-dimensional figure. Let
Chapter 6, Problem 115SE(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 \(\lambda v\) The particles
might represent pollution particles in air, bacteria in water, or stars in the heavens.
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
\(f(r)=\left\{\begin{array}{ll} 4 \lambda \pi r^{2} e^{-(4 / 3) \lambda \pi r^{3}}, & r>0 \\ 0, & \text
{ elsewhere } \end{array}\right.\)
If R is as in part (a), show that \(U=R^{3}\) has an exponential distribution.
Equation Transcription:
{
Text Transcription:
\lambda v
f(r)={ 4 \lambda \pi r^2 e^-(4 / 3) \lambda \pi r^3, & r>0 0, & elsewhere
U=R^3
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer