Results 1 to 2 of 2

Math Help - Poisson distribution mean and variance

  1. #1
    Junior Member
    Joined
    Oct 2008
    Posts
    27

    Question Poisson distribution mean and variance

    Hi,

    I'm having trouble understanding the mean and variance for Poisson distribution problems.

    I have an example problem where patiens check-in to a clinic according to a Poisson distribution at a average of 7 patients per hour. Given that it takes approximately 10 minutes to see each patient, I need to find the mean and variance of the total service time for patients arriving during a 1h period (it can be assumed that there are enough doctors available so that no patients needs to wait to be seen).

    The answers given are E[S]=7 and V[S]=700 but I can't understand why...

    If it takes 10 minutes to see each patient, how can the mean of the total service time be less than 10 minutes?

    Also, I thought that with Poisson distributions, E[S]=V[S]=lambda, so why are they different here?

    Thanks,

    Paul
    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 Canadian0469 View Post
    Hi,

    I'm having trouble understanding the mean and variance for Poisson distribution problems.

    I have an example problem where patiens check-in to a clinic according to a Poisson distribution at a average of 7 patients per hour. Given that it takes approximately 10 minutes to see each patient, I need to find the mean and variance of the total service time for patients arriving during a 1h period (it can be assumed that there are enough doctors available so that no patients needs to wait to be seen).

    The answers given are E[S]=7 and V[S]=700 but I can't understand why...

    If it takes 10 minutes to see each patient, how can the mean of the total service time be less than 10 minutes?

    Also, I thought that with Poisson distributions, E[S]=V[S]=lambda, so why are they different here?

    Thanks,

    Paul
    Let X be the random variable number of patients in one hour and S the random variable service time for patients in a one hour period.

    Then S = 10X.

    So I'd have thought that E(S) = (10) (7) = 70 minutes (in other words, I'd suggest the given answers contain a typo) and Var(S) = (10^2)(7) = 700 (=> sd(S) = 26.5 minutes).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Calculating Variance - Poisson process
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: March 24th 2011, 03:13 PM
  2. need help variance of poisson dist.
    Posted in the Advanced Statistics Forum
    Replies: 7
    Last Post: July 26th 2010, 03:48 AM
  3. Variance in poisson process
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: February 23rd 2010, 08:02 PM
  4. Poisson Distribution - Expressing Variance that is free of Mu.
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: November 10th 2009, 12:51 PM
  5. [SOLVED] Variance of the poisson distribution
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: February 24th 2009, 10:20 AM

Search Tags


/mathhelpforum @mathhelpforum