Statistics The gamma distribution

[vanitymdl]

Homework Statement

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?

 

[Dustinsfl]

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

 

[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"

 

[Ray Vickson]

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"

See your textbook or course notes. If that does not work, see, eg.,
http://en.wikipedia.org/wiki/Probability_density_function .

RGV

 

[uart]

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"

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).

 

[Dustinsfl]

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

 

[Ray Vickson]

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

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