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Math Help - Gamma Distribution

  1. #1
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    Gamma Distribution

    Annual incomes for heads of household in a section of a city have approximately a gamma distribution with alpha = 20 and beta = 1000.

    a) Find the mean and the variance of these incomes

    b) Would you expect to find many incomes in excess of $30,000 in this section of the city?

    For a) Mean = (alpha)(beta) = (20)(1000) = 20000
    Variance = (alpha)(beta)^2 = (20)(1000)^2 = 20000000
    Is this correct?

    For b) I'm not sure how to go about this. Any advice?

    Thanks!!
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  2. #2
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    Quote Originally Posted by jzellt View Post

    For a) Mean = (alpha)(beta) = (20)(1000) = 20000
    Variance = (alpha)(beta)^2 = (20)(1000)^2 = 20000000
    Is this correct?

    For b) I'm not sure how to go about this. Any advice?

    Thanks!!
    Your part a) is correct.

    For part b) find P(X>30000) = 1-P(X<30000).

    Now apply the cdf for the gamma distribution.
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  3. #3
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    Not sure what to use here. Can you show?
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  4. #4
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    The best way to do a cdf calc for the Gamma dist is using technology. I would use the excel function =GAMMADIST(30000,20,1000,1). There is also many probability calculators on the net that will help.

    If you must find it by hand then the cdf can be found here.

    Gamma distribution
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  5. #5
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    I guess Im still not understanding. Can anyone show how to calculate 1 - P(Y < 30000)? Thanks
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