1. ## 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?

Thanks!!

2. Originally Posted by jzellt

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

Thanks!!

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

Now apply the cdf for the gamma distribution.

3. Not sure what to use here. Can you show?

4. 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

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