# Gamma Distribution problem

## Main Question or Discussion Point

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..

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