Results 1 to 12 of 12

Math Help - poisson probability

  1. #1
    Junior Member
    Joined
    Aug 2007
    Posts
    71

    poisson probability

    The number of oil tankers arriving at a refinery each day has a Poisson distribution with parameter  \lambda = 3 . Current port facilities can service only four tankers a day so that if more than four tankers arrive in a day, the additional tankers must be sent to another port.

    What is the expected number of tankers serviced daily at the current port facilities?

    Is is simply  3 ? The other information is extraneous?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by lord12 View Post
    The number of oil tankers arriving at a refinery each day has a Poisson distribution with parameter  \lambda = 3 . Current port facilities can service only four tankers a day so that if more than four tankers arrive in a day, the additional tankers must be sent to another port.

    What is the expected number of tankers serviced daily at the current port facilities?

    Is is simply  3 ? The other information is extraneous?
    No:

    E(N)=p(0) \times 0 + p(1) \times 1+ p(2) \times 2 + p(3) \times 3 + p(n\ge 4) \times 4 \ne 3

    ( p(n \ge 4) = 1-(p(0)+p(1)+p(2)+p(3)))

    Where p(n) is the probability that n tankers arrive in a day.

    The sum is truncated at 4 because if anymone than 4 tankers arrive they are not serviced.

    RonL
    Last edited by CaptainBlack; September 25th 2008 at 04:24 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Aug 2007
    Posts
    71
    I don't understand. then, why for a Possion Random Variable, the expected value and variance is always equal to lambda.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by lord12 View Post
    I don't understand. then, why for a Possion Random Variable, the expected value and variance is always equal to lambda.
    The number serviced is not a poisson RV, but it is truncated, all the ships after the 4th are sent away and so not serviced. So ther properties of the poisson distribution are only indirectly involved, and then by explicit calculation of the expectation.

    RonL
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Aug 2007
    Posts
    71
    So if as n approaches infinity, the expected value approaches lambda?
    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 lord12 View Post
    I don't understand. then, why for a Possion Random Variable, the expected value and variance is always equal to lambda.
    The number arriving has a Poisson distribution. But this is a different random variable to the number serviced.

    It's the expected value of the number arriving that's equal to 3. Not the number serviced.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    May 2008
    Posts
    21

    Add-on challenging math question

    I'd like to add on another part to the question. Suppose lambda is 1.5 and present port facilities can service three tankers a day. If more than 3 tankers arrive in a day, the tankers in excess of 3 must be sent to another port.

    How much must present facilities be increased to permit handling all arriving tankers on approximately 90per cent of the days?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by math beginner View Post
    I'd like to add on another part to the question. Suppose lambda is 1.5 and present port facilities can service three tankers a day. If more than 3 tankers arrive in a day, the tankers in excess of 3 must be sent to another port.

    How much must present facilities be increased to permit handling all arriving tankers on approximately 90per cent of the days?
    Let the numer that can be serviced per day at the expanded port be n.

    The the question asks what is the smallest n be so that

    \sum_{i=1}^n p(i)<0.9

    where p(i) is the the probability of i arrivals in a day.

    Now try this for n=0,1,2,3,..

    RonL
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie
    Joined
    May 2008
    Posts
    21

    Clarification

    I am so sorry, I am not clear about the p(i). Could you explain?
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by math beginner View Post
    I am so sorry, I am not clear about the p(i). Could you explain?
    You are told that the number of arrivals per day has a Poisson distribution so:

    p(i)=f(i,\lambda)=\frac{\lambda^ie^{-lambda}}{i!}

    You are told tha \lambda=1.5

    RonL
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Newbie
    Joined
    May 2008
    Posts
    21

    still stuck

    sorry i'm still stuck. i calculate poisson probability for i=0 + i=1 + i=2 + i=3 and already the cumulative probability is 0.9344. The current capacity of 3 tankers is already serving 90% of the tankers. The question asks how much must present facilities be increased so as to serve all the tankers 90% of the time...my calculation suggest that they do not need to increase facilities. Something is wrong...please could you help?
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by math beginner View Post
    sorry i'm still stuck. i calculate poisson probability for i=0 + i=1 + i=2 + i=3 and already the cumulative probability is 0.9344. The current capacity of 3 tankers is already serving 90% of the tankers. The question asks how much must present facilities be increased so as to serve all the tankers 90% of the time...my calculation suggest that they do not need to increase facilities. Something is wrong...please could you help?
    That's what my calculations indicate as well.

    RonL
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Poisson probability
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: March 22nd 2011, 01:01 AM
  2. Probability - Poisson
    Posted in the Statistics Forum
    Replies: 3
    Last Post: November 8th 2010, 02:19 PM
  3. Poisson Probability
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: June 21st 2010, 08:37 AM
  4. Probability (Poisson)
    Posted in the Statistics Forum
    Replies: 2
    Last Post: December 16th 2009, 08:00 PM
  5. poisson probability
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: March 12th 2009, 10:20 PM

Search Tags


/mathhelpforum @mathhelpforum