# Statistics! The gamma distribution

1. Nov 11, 2012

### vanitymdl

1. The problem statement, all variables and given/known data
Find the probabilities that the value of a random variable will exceed 4 if it has a gamma distribution with
(a) $\alpha$ = 2 and $\beta$ = 3
(b) $\alpha$ = 3 and $\beta$ = 4

3. The attempt at a solution[/b}
how would I even attempt this question?

2. Nov 11, 2012

### Dustinsfl

What is your definition of the gamma distribution? Is it defined with alpha and beta? If so, plug it in and solve.

3. Nov 11, 2012

### vanitymdl

The gamma distribution that is given includes an "x". How am supposed to solve for this equation when it doesn't give me an "X"

4. Nov 12, 2012

### Ray Vickson

5. Nov 12, 2012

### uart

You need to have access to the incomplete gamma function (integral) or tables to compute the cumulative distribution function. Just be careful with the second parameter ($\beta$) as some tables/functions will use the reciprocal value here (eg 1/3 instead of 3).

6. Nov 12, 2012

### Dustinsfl

$$\frac{\beta^{\alpha}}{\Gamma(\alpha)}x^{\alpha - 1}e^{-\beta x}$$

7. Nov 12, 2012

### Ray Vickson

I think the issue is that *some* sources give
$$\frac{1}{\beta^{\alpha}\: \Gamma(\alpha)} x^{\alpha -1} e^{-x/ \beta},$$
so the OP needs to check, not assume.

RGV