d2j2003
Oct5-11, 02:01 PM
In a certain country, the distribution of incomes in thousands of dollars is described by a gamma distribution with \alpha = 2 and \beta = 8. What is the probability that a man chosen at random will have the following incomes?
a. More than $14,000
b. At least $12,000
So I know that f(x;\alpha,\beta) = \frac{1}{\Gamma(\alpha)\beta^{\alpha}}x^{\alpha-1}e^{-x/\beta} for x>0,\alpha,\beta>0
and \Gamma(\alpha)=\int^{\infty}_{0}xe^{-x} = 1
so f(x) = \frac{1}{64} xe^{-x/8}
Not sure where to go from here though.. Hopefully i'm heading in the right direction..
a. More than $14,000
b. At least $12,000
So I know that f(x;\alpha,\beta) = \frac{1}{\Gamma(\alpha)\beta^{\alpha}}x^{\alpha-1}e^{-x/\beta} for x>0,\alpha,\beta>0
and \Gamma(\alpha)=\int^{\infty}_{0}xe^{-x} = 1
so f(x) = \frac{1}{64} xe^{-x/8}
Not sure where to go from here though.. Hopefully i'm heading in the right direction..