Results 1 to 13 of 13

Math Help - Poisson random variable

  1. #1
    Member
    Joined
    Nov 2008
    From
    MD
    Posts
    165

    Exclamation Poisson random variable

    Suppose that the number of accidents occurring on a highway each day is a Poisson random variable with the expected number of accidents a day equaling 3. Find the probability that 3 or more accidents occur today. Then, find the probability that 3 or more accidents occur today under the assumption that at least 1 accident occurs today.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by holly123 View Post
    Suppose that the number of accidents occurring on a highway each day is a Poisson random variable with the expected number of accidents a day equaling 3. Find the probability that 3 or more accidents occur today. Then, find the probability that 3 or more accidents occur today under the assumption that at least 1 accident occurs today.
    The first part is simple substitution into the pmf: \Pr(X \geq 3) = 1 - \Pr(X \leq 2).

    The second part is conditional probability: \displaystyle \Pr(A | B) = \frac{\Pr(A \cap B)}{\Pr(B)}. Again, all that's required now is simple substitution into the pmf. Note that \Pr(X \geq 1) = 1 - \Pr(X = 0).

    If you need more help, please show your work and say where you get stuck.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Nov 2008
    From
    MD
    Posts
    165
    The whole "Poisson" thing is throwing me off. How do I find probabilities such as X less than or equal to 2?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by holly123 View Post
    The whole "Poisson" thing is throwing me off. How do I find probabilities such as X less than or equal to 2?
    Have you studied the Poisson distribution? It is odd that you would be given a question about it if you have not studied it.

    Have you looked up the pmf in your textbook or used Google?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Nov 2008
    From
    MD
    Posts
    165
    We just started it today so I'm very new to it. I'm trying looking at my book and google but I think it's only confusing me more. Google says probability is P(X = k) = e ^(- ) * ^k / k!
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by holly123 View Post
    [snip]
    Google says probability is P(X = k) = e ^(- ) * ^k / k!
    Yes. Now apply it.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Nov 2008
    From
    MD
    Posts
    165
    So 1- Pr(0) + Pr(1) + Pr(2)= 1-(e^-3 +3e^-3 + 9/2 e^-3)
    Is that right so far?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by holly123 View Post
    So 1- Pr(0) + Pr(1) + Pr(2)= 1-(e^-3 +3e^-3 + 9/2 e^-3)
    Is that right so far?
    Yes. (Why would it not be?)
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie
    Joined
    Oct 2010
    Posts
    3
    Quote Originally Posted by mr fantastic View Post
    Yes. (Why would it not be?)
    Hi

    I'm having the same problem trying to grasp Poisson.
    I don't see how you got from

    P(X = k) = e ^(- ) * ^k / k!

    to

    1- Pr(0) + Pr(1) + Pr(2)= 1-(e^-3 +3e^-3 + 9/2 e^-3)

    could you please explain
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by unterglayben View Post
    Hi

    I'm having the same problem trying to grasp Poisson.
    I don't see how you got from

    P(X = k) = e ^(- ) * ^k / k!

    to

    1- Pr(0) + Pr(1) + Pr(2)= 1-(e^-3 +3e^-3 + 9/2 e^-3)

    could you please explain
    Did you try substituting the given mean and the values of k into the pmf?
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Newbie
    Joined
    Oct 2010
    Posts
    3
    Hi

    Thanks for getting back to me.

    I got this online for the pmf of a poisson.



    I still don't see how you get

    1- Pr(0) + Pr(1) + Pr(2)= 1-(e^-3 +3e^-3 + 9/2 e^-3)

    could you provide me with the formula into which I sub the values please. I see that on the left it's each value for the probability up to and including 3 and then subtract from 1 to get probability of greater than or equal to 4, but the 9/2 on the right hand side of the equation? No idea where that came from.
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Newbie
    Joined
    Oct 2010
    Posts
    3
    Sorry, I was using the values from my problem. I meant, I see the left side as being the values to figure out less than or equal to 2.
    Follow Math Help Forum on Facebook and Google+

  13. #13
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by unterglayben View Post
    Hi

    Thanks for getting back to me.

    I got this online for the pmf of a poisson.



    I still don't see how you get

    1- Pr(0) + Pr(1) + Pr(2)= 1-(e^-3 +3e^-3 + 9/2 e^-3)

    could you provide me with the formula into which I sub the values please. I see that on the left it's each value for the probability up to and including 3 and then subtract from 1 to get probability of greater than or equal to 4, but the 9/2 on the right hand side of the equation? No idea where that came from.
    Substitute \lambda = 3 and k = 2 into the pmf.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: October 15th 2012, 10:37 PM
  2. poisson random variable
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: March 2nd 2011, 05:13 PM
  3. Poisson random variable?
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: April 13th 2009, 06:50 PM
  4. Poisson Random Variable
    Posted in the Statistics Forum
    Replies: 1
    Last Post: March 29th 2009, 12:06 AM
  5. Poisson random variable
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: February 24th 2009, 03:23 AM

Search Tags


/mathhelpforum @mathhelpforum