1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Poisson Process question

  1. Feb 24, 2010 #1
    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]
     
  2. jcsd
  3. Feb 24, 2010 #2
    I believe that this is correct. If X Y and Z are independent then a random variable say A=X+Y+Z would have a poisson distribution with rate of [tex]\lambda_X[/tex] +[tex]\lambda_Y[/tex]+[tex]\lambda_Z[/tex]
    Although you initially wrote [tex]\lambda_Z[/tex] =3 ,but put down 4.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook