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Probability Question About The Poisson Probability Distribution

  1. Mar 16, 2010 #1
    Probability Question About "The Poisson Probability Distribution"

    1. The problem statement, all variables and given/known data - Assume that 1 in 200 people carry the defective gene that causes inherited colon cancer. A sample of 1000 individuals is taken.

    Use the Poisson approximation to calculate the appoximate standard deviation of the number of people who carry the gene.


    2. Relevant equations



    3. The attempt at a solution I am honestly having a hard time even getting started with this one. I think I find Lamda by setting 1-[tex]e^{-\lambda1000}[/tex]=1/2
     
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  3. Mar 16, 2010 #2

    Dick

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    Re: Probability Question About "The Poisson Probability Distribution"

    What does it say lambda is in the definition of a Poisson distribution?
     
  4. Mar 16, 2010 #3
    Re: Probability Question About "The Poisson Probability Distribution"

    It says that Lamda is "frequently a rate per unit time or per unit area".
     
  5. Mar 16, 2010 #4

    Dick

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    Re: Probability Question About "The Poisson Probability Distribution"

    That's not helpful. You could describe a lot of things that way. Nothing more specific? Check wikipedia if your reference is completely lame.
     
  6. Mar 16, 2010 #5
    Re: Probability Question About "The Poisson Probability Distribution"

    It also says that lamda is equal to n*p. I think I need to use the entire population (1000) for n. But I have no idea what to use for 'p'.
     
  7. Mar 16, 2010 #6

    Dick

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    Re: Probability Question About "The Poisson Probability Distribution"

    Maybe 'p' has something to do with '1 in 200'.
     
  8. Mar 16, 2010 #7
    Re: Probability Question About "The Poisson Probability Distribution"

    According to Wikipedia: "λ is a positive real number, equal to the expected number of occurrences that occur during the given interval. For instance, if the events occur on average 4 times per minute, and you are interested in the number of events occurring in a 10 minute interval, you would use as your model a Poisson distribution with λ = 10×4 = 40".

    So it looks like lamda = 1000*1/200 = 5 (if I'm understanding this)
     
  9. Mar 16, 2010 #8

    Dick

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    Re: Probability Question About "The Poisson Probability Distribution"

    You are understanding correctly.
     
  10. Mar 16, 2010 #9
    Re: Probability Question About "The Poisson Probability Distribution"

    Okay, cool. That gets me started then. I'll see what I can drum up here. Thanks for your help.
     
  11. Mar 16, 2010 #10
    Re: Probability Question About "The Poisson Probability Distribution"

    So it looks likeE(X) = V(X) = Lamda. So finding the standard deviation should be as simple as finding the square root of five right?
     
  12. Mar 16, 2010 #11

    Dick

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    Re: Probability Question About "The Poisson Probability Distribution"

    Yes, it's that simple. Do you know why it's only the 'approximate' standard deviation for a sample of 1000?
     
  13. Mar 16, 2010 #12
    Re: Probability Question About "The Poisson Probability Distribution"

    I'm assuming it is because the square root of five is an irrational number.
     
  14. Mar 16, 2010 #13
    Re: Probability Question About "The Poisson Probability Distribution"

    Gotta get to class. Thanks for helping me. I appreciate it.
     
  15. Mar 16, 2010 #14

    Dick

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    Re: Probability Question About "The Poisson Probability Distribution"

    No, it's because a Poisson distribution only 'approximates' a binomial distribution with a large sample size. For a binomial distribution V(X)=n*p*(1-p), but since 1-p is almost 1, you get almost the same thing. That's why they said 'approximate'. Just so you know.
     
  16. Mar 16, 2010 #15
    Re: Probability Question About "The Poisson Probability Distribution"

    Okay, got it. My teacher is just terrible. You have helped me more about this than pouring over this book, and every lecture that guy could ever give. Thanks again.
     
  17. Mar 16, 2010 #16

    Dick

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    Re: Probability Question About "The Poisson Probability Distribution"

    Sure. Nice of you to say. But I think you pore over a book, you don't pour over it. Pouring is kind of a strange image. But you are welcome!
     
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