# Poisson distribution

1. Mar 25, 2009

### superwolf

1. The problem statement, all variables and given/known data

In a Poisson process with intensity λ, let X1 be the time untill the first event and let X2 be the time between the first and the second event. Let Y be the time untill the second event, that is, Y = X1 + X2. Find the density function f(y).

2. The attempt at a solution

Probability that no events occur in time y:

$$p(0; \lambda X1) = e^{- \lambda t}$$

I don't know if this will be helpful at all...

2. Mar 25, 2009

### Focus

I'll give you a hint, the holding times (time between two jumps) of a Poisson process are independent and exponential with parameter lambda. You may want to prove this.