Gamma Distribution Help!!

statman101 · #1 $Old$ October 30th, 2009, 11:20 AM

Suppose the reaction time X of a randomly selected individual to a certain stimulus is a standard gamma distribution with (alpha=2)

What is F(5;2) using gamma

show steps i dont understand!

theodds · #2 $Old$ October 30th, 2009, 11:39 AM

I'm guessing by standard gamma they mean the scale parameter (i.e. beta) is equal to 1. Since alpha = 2, we can just write down the density $f_X (x) = \frac{1}{\Gamma(2)} x^{2 - 1}e^{-x} = xe^{-x}$ . You can solve for F(x) in the usual way using integration by parts. If you haven't had calculus, or are just being blindsided by this (since this is the pre-university forum), just post so and I'll give a different explanation (at some point, I have to go to class).

statman101 · #3 $Old$ October 30th, 2009, 12:36 PM

you put 2 in for x, but didnt put 2 in for e^-x

theodds · #4 $Old$ October 30th, 2009, 01:17 PM

Nah, I put in 2 for alpha everywhere. Or are you talking about the exponential not having a parameter? That is where beta would normally be, but since it's 1, it's just $e^{-x}$ . Just to be sure we're clear, the density for a Gamma(alpha, beta) is $f(x) = \frac{1}{\Gamma(\alpha) \beta^{\alpha}} x^{\alpha - 1} e^{\frac{-x}{\beta}}$ . Plug 1 for beta and 2 for alpha and you get the density I posted.

statman101 · #5 $Old$ October 30th, 2009, 01:24 PM

can u show in steps the function evaluated at F(5;2)

its supposed to equal
.960

theodds · #6 $Old$ October 30th, 2009, 01:43 PM

To get F(5), use the fact that $F(x) = \int_0 ^{x} f(t)dt$ . I did this and got .960. After integration by parts you get $F(x) = 1 - e^{-x}(x + 1)$