# Gamma Distribution

• Jul 18th 2009, 10:47 PM
MathRules!
Gamma Distribution
Hi, I need help with the following:

If X has the gamma distribution with θ = 4 and α = 2, find P(X < 5).

So far I have plugged in the numbers into the formula, but I am not sure if what I am doing is correct.

f(x) = [1/(Γ(2)4^2]x^(2-1)e^(-x/4)

Does Γ(2) have a value?

afterwards should I integrate f(x) from -infinity to 5?
• Jul 18th 2009, 11:03 PM
CaptainBlack
Quote:

Originally Posted by MathRules!
Hi, I need help with the following:

If X has the gamma distribution with θ = 4 and α = 2, find P(X < 5).

So far I have plugged in the numbers into the formula, but I am not sure if what I am doing is correct.

f(x) = [1/(Γ(2)4^2]x^(2-1)e^(-x/4)

Does Γ(2) have a value?

afterwards should I integrate f(x) from -infinity to 5?

\$\displaystyle \Gamma(x)\$ is the gamma function which for positive integer arguments is related to the factorial by:

\$\displaystyle \Gamma(n)=(n-1)!\$

so:

\$\displaystyle \Gamma(2)=(2-1)!=1!=1\$

CB