(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Events X, Y, Z are all Poisson processes. Event X has a rate of 1 per unit time , event Y has a rate of 2 per unit time and event Z has a rate of 3 per unit time.

Find the probability that 2 events (of any type) occur during the interval (0, 3).

2. Relevant equations

Maybe this is relevant

P(N=k) = [tex]\frac{(\lambda t)^k e^{-\lambda t}}{k!}[/tex]

3. The attempt at a solution

So [tex]\lambda_X[/tex] = 1, [tex]\lambda_Y[/tex] = 2 and [tex]\lambda_Z[/tex] = 4. Also k = 2 and t =3.

Is it correct to think of it as say A = X [tex]\cup[/tex] Y [tex]\cup[/tex] Z. Then the answer is:

P(N=2) = [tex]\frac{(7(3))^2 e^{-7(3)}}{2!}[/tex] where [tex]\lambda_A = 1 + 2 + 4 = 7. [/tex]

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# Homework Help: Poisson Process question

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