Poisson processes

**adnaps1** · December 9th 2010, 12:47 AM

A radioactive source emits particles according to a Poisson process with rate $\lambda=2$ particles per minute. What is the expected time of emission of the second particle given that three particles have been emitted in the first four minutes?

**CaptainBlack** · December 9th 2010, 03:01 AM

Originally Posted by adnaps1

A radioactive source emits particles according to a Poisson process with rate $\lambda=2$ particles per minute. What is the expected time of emission of the second particle given that three particles have been emitted in the first four minutes?

Use Bayes theorem to find: $P(t_2|t_4\le 4)$ then the expected time of emmision of the second particle is:

$\displaystyle \int_0^4 t_2 P(t_2|t_4\le 4)\ dt_2$

CB

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