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Poisson distribution

  • Thread starter superwolf
  • Start date
1. Homework Statement

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:

[tex]
p(0; \lambda X1) = e^{- \lambda t}
[/tex]

I don't know if this will be helpful at all...
 
280
1
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.
 

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