Results 1 to 12 of 12

Math Help - Distribution of Poison

  1. #1
    Super Member
    Joined
    Jun 2008
    Posts
    829

    Distribution of Poison

    A dealership sells an average of 0.5 cars per day. The company needs to pay a debt that matures in two days. Must sell at least three cars in two days, what is the likelihood that the company can pay the debt?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jul 2009
    Posts
    593
    Thanks
    4
    If the company sells 0.5 cars in one day, how many cars do they sell over two days?

    Once you make that transformation, it is simply a matter of plugging and chugging into the formula for the Poisson distribution.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Jun 2008
    Posts
    829
    Quote Originally Posted by ANDS! View Post
    If the company sells 0.5 cars in one day, how many cars do they sell over two days?

    Once you make that transformation, it is simply a matter of plugging and chugging into the formula for the Poisson distribution.
    Ok. I find:

    \frac{e^{-1} 1^3}{3!} = 0,06131
    But the answer is: 0,0803
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Jul 2009
    Posts
    593
    Thanks
    4
    Well the company must sell at LEAST 3 cars. Not exactly 3 cars. The probability that they sell exactly three cars is 0.0613. How would you go about finding the probability that they sell at LEAST 3 cars; we are still using Poisson here, but you're going to have to take the compliment of something.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    Joined
    Jun 2008
    Posts
    829
    Quote Originally Posted by ANDS! View Post
    Well the company must sell at LEAST 3 cars. Not exactly 3 cars. The probability that they sell exactly three cars is 0.0613. How would you go about finding the probability that they sell at LEAST 3 cars; we are still using Poisson here, but you're going to have to take the compliment of something.
    I understand. Can sell more than three cars. But I do not know how to calculate this probability
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member
    Joined
    Jul 2009
    Posts
    593
    Thanks
    4
    Well if they can sell more than 3 cars, then theoretically they can sell 100 cars or 1000 cars or "n" number of cars. So to find out the Poisson Distribution of "at least 3 cars. . ." you would have to calculate Poisson(3)+Poisson(4)+Poisson(5)+. . .Poisson(n). Of course this isn't possible (or how you're supposed to do this). Thus you need another alternative.

    As I said, you can use the idea of the compliment of an event. If they don't sell at LEAST 3 cars in two days, then how many cars at MOST did they sell. Find the Poisson Distribution of the AT MOST statement, and see if something clicks.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Super Member
    Joined
    Jun 2008
    Posts
    829
    Quote Originally Posted by ANDS! View Post
    Well if they can sell more than 3 cars, then theoretically they can sell 100 cars or 1000 cars or "n" number of cars. So to find out the Poisson Distribution of "at least 3 cars. . ." you would have to calculate Poisson(3)+Poisson(4)+Poisson(5)+. . .Poisson(n). Of course this isn't possible (or how you're supposed to do this). Thus you need another alternative.

    As I said, you can use the idea of the compliment of an event. If they don't sell at LEAST 3 cars in two days, then how many cars at MOST did they sell. Find the Poisson Distribution of the AT MOST statement, and see if something clicks.
    I was adding: P(3) + P(4) + P(5) + P(6) + .....
    I checked that was approaching to 0,0803. But, how can I be sure? I find answer < 0,0803 and answer > 0,0803
    Last edited by Apprentice123; June 3rd 2010 at 02:34 PM.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Super Member
    Joined
    Jul 2009
    Posts
    593
    Thanks
    4
    Do this for me, find that Probability that they sell at most 2 cars (meaning they might sell 0, 1 or 2 cars). Let me know what you get.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Super Member
    Joined
    Jun 2008
    Posts
    829
    Quote Originally Posted by ANDS! View Post
    Do this for me, find that Probability that they sell at most 2 cars (meaning they might sell 0, 1 or 2 cars). Let me know what you get.
    Knowing the probability of paying the debt. To pay the debt has to sell at least 2 cars, then P (> = 2)

    How to get an exact answer, if P(2) + P(3) + .... ???
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1
    Apprentice, you know the Poisson formula. Add them up from 0 to 2 and subtract from 1.

    They say at least 3 must be sold. That can be 3 up to however many.

    But, since there is no given bound, find the probabilties from 0 to 2 and subtract from 1.

    1-\sum_{k=0}^{2}\frac{e^{-1}}{k!}

    Because {\lambda}=.5(2)=1
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Super Member
    Joined
    Jun 2008
    Posts
    829
    Quote Originally Posted by galactus View Post
    Apprentice, you know the Poisson formula. Add them up from 0 to 2 and subtract from 1.

    They say at least 3 must be sold. That can be 3 up to however many.

    But, since there is no given bound, find the probabilties from 0 to 2 and subtract from 1.

    1-\sum_{k=0}^{2}\frac{e^{-1}}{k!}

    Because {\lambda}=.5(2)=1
    Ohhh yes. Thank you
    Follow Math Help Forum on Facebook and Google+

  12. #12
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    depends on how much poison you take
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. normal distribution prior and posterior distribution proof
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: March 9th 2011, 07:12 PM
  2. Replies: 2
    Last Post: March 29th 2010, 03:05 PM
  3. Mixture of Gamma, Poison, and Pareto Distribution
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: October 7th 2009, 02:19 PM
  4. General poison process question
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: April 21st 2009, 05:45 AM
  5. Poison distribution
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: September 28th 2006, 06:34 PM

Search Tags


/mathhelpforum @mathhelpforum