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Math Help - Probability for estimate/poisson distribution

  1. #1
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    Probability for estimate/poisson distribution

    Hi

    I've searched the forum for topic but I can't seem find one with the same problem, so here goes:

    I have Xi given as the number of an occurrence pr quarter.

    X1...Xn is independent and Xi~Poisson(a)

    I have maximized a for the likelihoodfunction to be [LaTeX ERROR: Convert failed] as an estimation of a.

    Now to my question:
    For a=1.25 and n=10, what is the probability that a* equals respectively 1.1 and 1.25?

    My paper is to be done in a couple of hours, so help would be very much appreciated..

    Edit: Even though the couple of hours has gone by, I actually still need som help, so if anyone have a hint or two..?
    Last edited by iljitj; May 6th 2008 at 01:26 PM.
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  2. #2
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    Quote Originally Posted by iljitj View Post
    Hi

    I've searched the forum for topic but I can't seem find one with the same problem, so here goes:

    I have Xi given as the number of an occurrence pr quarter.

    X1...Xn is independent and Xi~Poisson(a)

    I have maximized a for the likelihoodfunction to be a*=\frac{1}{n}\sum{Xi} as an estimation of a.

    Now to my question:
    For a=1.25 and n=10, what is the probability that a* equals respectively 1.1 and 1.25?

    My paper is to be done in a couple of hours, so help would be very much appreciated..

    Edit: Even though the couple of hours has gone by, I actually still need som help, so if anyone have a hint or two..?
    The sum of n Poisson iid RV's with parameter a, is a Poission RV with parameter na.

    RonL
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  3. #3
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    Thanks for replying

    Correct me if I'm wrong, but does that mean that I should do it like this:

    P(X=1.1)=\frac{12.5^{11}}{11!}e^-12.5=0.109

    ??
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by iljitj View Post
    Thanks for replying

    Correct me if I'm wrong, but does that mean that I should do it like this:

    P(X=1.1)=\frac{12.5^{11}}{11!}e^{-12.5}=0.109

    ??
    Yes

    RonL
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