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: Merging Poisson Distributions

  1. Aug 6, 2006 #1
    Consider a poisson process one (P1) with a frequency 'a' and if it happens 'k' times you get (e^-a)(a^k)/k!

    and then you have another posssion processs that happens in the same time frame of P1 called P2 with a frequency of 'b' and if it happens 'z' times you get (e^-b)(b^z)/z!

    So what is the probability that P1 merges with P2?

    For example if is observed that a computer breaks once every 2 days and a lightbulb goes out every 4 days what is the probability that in one week two computers will break at the exact same time 5 lightbulbs go out?

    I know this problem has something to do with the poisson distribution but I dont know how to merge these events to get an answer.

    I went to wikipedia and searched on the net and couldnt find any exmaples of such a problem that deals with two events.

    I found somethign on wikipedia that says:

    If N and M are two independent random variables, both following a Poisson distribution with parameters λ and μ, respectively, then N + M follows a Poisson distribution with parameter λ + μ.

    I know the the probabilities of both events happening are less than the probability of just one, but I dont think you can just multiply the probability of event each together to get the final probability of both events happening at the same time.
    Last edited: Aug 6, 2006
  2. jcsd
  3. Aug 6, 2006 #2


    User Avatar
    Science Advisor

    If they are independent Poisson processes, you just multiply the probabilities. The probability that five lightbulbs will go out over a period of time in which two computers break is the probability that five lightbulbs go out over that period times the probability that two computers break. I don't know what you mean by "exact same time," unless you mean one week.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook