Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Let $N$ be a homogeneous Poisson process with intensity $\lambda$. How do I compute the following probability: $$P[N(5)=2 \, | \, N(2)=1,N(10)=3]?$$

share|cite|improve this question

You know that exactly $2$ events occurred between $t=2$ and $t=10$. These are independently uniformly distributed over the interval $[2,10]$. The probability that one of them occurred before $t=5$ and the other thereafter is therefore $2\cdot\frac38\cdot\frac58=\frac{15}{32}$. The intensity $\lambda$ doesn't enter into it, since you know the numbers of events.

share|cite|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.