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Statistics! The gamma distribution

  1. Nov 11, 2012 #1
    1. The problem statement, all variables and given/known data
    Find the probabilities that the value of a random variable will exceed 4 if it has a gamma distribution with
    (a) [itex]\alpha[/itex] = 2 and [itex]\beta[/itex] = 3
    (b) [itex]\alpha[/itex] = 3 and [itex]\beta[/itex] = 4

    3. The attempt at a solution[/b}
    how would I even attempt this question?
     
  2. jcsd
  3. Nov 11, 2012 #2
    What is your definition of the gamma distribution? Is it defined with alpha and beta? If so, plug it in and solve.
     
  4. Nov 11, 2012 #3
    The gamma distribution that is given includes an "x". How am supposed to solve for this equation when it doesn't give me an "X"
     
  5. Nov 12, 2012 #4

    Ray Vickson

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  6. Nov 12, 2012 #5

    uart

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    You need to have access to the incomplete gamma function (integral) or tables to compute the cumulative distribution function. Just be careful with the second parameter ([itex]\beta[/itex]) as some tables/functions will use the reciprocal value here (eg 1/3 instead of 3).
     
  7. Nov 12, 2012 #6
    $$
    \frac{\beta^{\alpha}}{\Gamma(\alpha)}x^{\alpha - 1}e^{-\beta x}
    $$
     
  8. Nov 12, 2012 #7

    Ray Vickson

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    I think the issue is that *some* sources give
    [tex] \frac{1}{\beta^{\alpha}\: \Gamma(\alpha)} x^{\alpha -1} e^{-x/ \beta},[/tex]
    so the OP needs to check, not assume.

    RGV
     
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