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Math Help - Point Estimation help

  1. #1
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    Point Estimation help

    During each lecture in a statistics class, let X equal the number of times that Professor Tanis collides with a computer table at the front of the classroom. Assume that the distribution of X is Poisson with a mean (lambda).

    (a) Given n observations of X, find the method of moments estimate of (lambda)
    (b) Give a point estimate of (lambda) using the following 11 observations of X that were collected by Chris:

    1,0,1,3,3,0,2,2,4,1,1


    I could use some direction with this problem....I keep looking through this put together book my professor is constructing with no luck on how to even go about starting to solve this problem.
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  2. #2
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    Quote Originally Posted by isuckatprobability View Post
    During each lecture in a statistics class, let X equal the number of times that Professor Tanis collides with a computer table at the front of the classroom. Assume that the distribution of X is Poisson with a mean (lambda).

    (a) Given n observations of X, find the method of moments estimate of (lambda)
    (b) Give a point estimate of (lambda) using the following 11 observations of X that were collected by Chris:

    1,0,1,3,3,0,2,2,4,1,1


    I could use some direction with this problem....I keep looking through this put together book my professor is constructing with no luck on how to even go about starting to solve this problem.
    In this question, the Method of Moments says that the mean of the n observations is assumed to be a reasonable estimate for the mean of X ....
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    for the first part I think I might have gotten it right..I used n = 18, lambda = 1/18*[0(1)+1(0)+2(1)+3(3)+4(3)+5(0)+6(2)+7(2)+8(4)+9(1)+ 10(1)] = 5.55 not sure if I did it right though
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  4. #4
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    Quote Originally Posted by isuckatprobability View Post
    for the first part I think I might have gotten it right..I used n = 18, lambda = 1/18*[0(1)+1(0)+2(1)+3(3)+4(3)+5(0)+6(2)+7(2)+8(4)+9(1)+ 10(1)] = 5.55 not sure if I did it right though
    Where has this data come from if n = 18 .......? Be that as it may, it's not difficult to calculate the mean value of a set of data. And that's all you have to do in this question ....
    Last edited by mr fantastic; November 20th 2008 at 10:15 PM. Reason: Added the n = 18.
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    Quote Originally Posted by isuckatprobability View Post
    for the first part I think I might have gotten it right..I used n = 18, lambda = 1/18*[0(1)+1(0)+2(1)+3(3)+4(3)+5(0)+6(2)+7(2)+8(4)+9(1)+ 10(1)] = 5.55 not sure if I did it right though
    It can't be right as the mean should not be larger than any of the observations.

    You have 18 collisions in 11 observations, the mean is 18/11

    CB
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  6. #6
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    I thought the total # of observations was 18. I found an example that shows them using the equation sum(xi)/n for a poisson distribution...
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  7. #7
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    forget it...I think that equation is for point estimation for lambda...I think you may be correct for part a
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