Results 1 to 7 of 7

Math Help - Help with Poisson Distribution!

  1. #1
    Newbie
    Joined
    Mar 2009
    Posts
    17

    Help with Poisson Distribution!

    The mean of a Poisson random variable X is μ = 9. Compute
    P(μ-2σ < X < μ + 2σ).


    My reasoning is as follows:
    P(9-2(9) < X < 9 + 2(9)) = P(-9 < X <27) . This is all I can think about doing at the moment. Feedback would be appreciated.
    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 MathRules! View Post
    The mean of a Poisson random variable X is μ = 9. Compute
    P(μ-2σ < X < μ + 2σ).


    My reasoning is as follows:
    P(9-2(9) < X < 9 + 2(9)) = P(-9 < X <27) . This is all I can think about doing at the moment. Feedback would be appreciated.
    \sigma^2 = 9 \Rightarrow \sigma = \sqrt{9} = 3.

    Calculate \Pr(3 < X < 15) = \Pr(4 \leq  X \leq 14). There's no easy way of doing this by hand - you just have to calculate each probability and then add them all up.

    You might be able to use the rule of thumb .... It will depend on what accuracy is required.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    Most books have tables of the Possion.
    This would be F(14)-F(3),
    where you need to find the \lambda=9 table.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Mar 2009
    Posts
    17
    Quote Originally Posted by mr fantastic View Post
    \sigma^2 = 9 \Rightarrow \sigma = \sqrt{9} = 3.

    Calculate \Pr(3 < X < 15) = \Pr(4 \leq  X \leq 14). There's no easy way of doing this by hand - you just have to calculate each probability and then add them all up.

    You might be able to use the rule of thumb .... It will depend on what accuracy is required.
    Ohh, I see.

    so I added the summation from 4 to 14 and have obtained that it is about 0.9373
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    That's correct to 4 places. F(14)=.9585 and F(3)=.0212.
    The difference is .9373. Note that
    F(14)=P(X=0)+P(X=1)+\cdots +P(X=14)
    and
    F(3)=P(X=0)+P(X=1)+P(X=2)+P(X=3).
    If you want to sum these 11 probabilities, one thing you should do is factor out the common term e^{-\lambda}
    Last edited by matheagle; March 10th 2009 at 11:18 PM.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Mar 2009
    Posts
    17

    Smile

    Quote Originally Posted by matheagle View Post
    That's correct to 4 places. F(14)=.9585 and F(3)=.0212.
    The difference is .9373. Note that
    F(14)=P(X=0)+P(X=1)+\cdots +P(X=14)
    and
    F(3)=P(X=0)+P(X=1)+P(X=2)+P(X=3).
    If you want to sum these 11 probabilities, one thing you should do is factor out the common term e^{-\lambda}
    Why didn't I think of that? ..... That is very smart! I will do that from now on.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    It's more experience than smart.
    That's why I make my students do the homework.
    I assign a lot, but I put those same problems on the exams and quizzes.
    They do their homework, they get good grades and I know they are learning. It works.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: December 27th 2011, 01:08 PM
  2. poisson distribution
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: February 7th 2011, 09:06 AM
  3. Poisson distribution and asymptotic normal distribution.
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: August 18th 2010, 05:52 AM
  4. poisson distribution
    Posted in the Statistics Forum
    Replies: 3
    Last Post: May 10th 2009, 12:36 PM
  5. Poisson Distribution HELP!!!
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: January 7th 2009, 04:06 AM

Search Tags


/mathhelpforum @mathhelpforum