Results 1 to 2 of 2

Math Help - Stochastic processes #2

  1. #1
    Junior Member
    Joined
    Oct 2008
    From
    Dallas, TX
    Posts
    71

    Stochastic processes #2

    On the average, Mr. Z drinks and drives once in 4 years. He knows that

    According to the laws of his state, the third time when he is caught drinking and driving results in the loss of his driver's license.

    Poisson process is the correct model for such ``rare events'' as drinking and driving.

    What is the probability that Mr. Z will keep his driver's license for at least 10 years?
    Last edited by mr fantastic; March 31st 2010 at 01:07 AM. Reason: Fixed formatting, edited post title
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Anonymous1's Avatar
    Joined
    Nov 2009
    From
    Big Red, NY
    Posts
    517
    Thanks
    1
    Let N(t)= the number of times Mr. Z gets pulled over by year t.

    Then N(t) is a poisson process with rate 1/4.

    Therefore N(t)=poi(t\times 1/4)

    Now, P(N(1)<3)= P(N(1)=1)+P(N(1)=2)

    \Rightarrow P(N(1)<3)= e^{-1/4}\frac{(1/4)^1}{1!} + e^{-1/4} \frac{(1/4)^2}{2!}

    By independent increments,

    \Rightarrow P(N(10)<3)= e^{-1/4\times 10}\frac{(1/4\times 10)^1}{1!} + e^{-1/4\times 10} \frac{(1/4\times 10)^2}{2!}

    I've been studying for my stochastic process test on monday .
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Stochastic processes #3
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: March 30th 2010, 10:44 PM
  2. need help - stochastic processes
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: March 21st 2010, 08:33 AM
  3. Stochastic Processes
    Posted in the Advanced Statistics Forum
    Replies: 7
    Last Post: December 10th 2009, 07:56 AM
  4. stochastic processes
    Posted in the Advanced Statistics Forum
    Replies: 6
    Last Post: September 28th 2009, 07:55 AM
  5. stochastic processes
    Posted in the Advanced Applied Math Forum
    Replies: 0
    Last Post: September 21st 2009, 12:22 PM

Search Tags


/mathhelpforum @mathhelpforum