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?
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.