Here's a probability question (probably really simple) I'm not sure how to solve:
Gamma distribution $X\sim \mathcal{G}(\alpha,\beta)$ with $\mu = 20$ and $\sigma^2 = 80$
$P(X \le 24)$ = ?
The previous question was finding the values of $\alpha$ and $\beta$, which I did using $\mu$ = $\alpha$$\beta$ and $\sigma^2$ = $\alpha$$\beta^2$.
For the gamma distribution cdf, my textbook says $P(X \le x) = F(x; \alpha, \beta) = F(x / \beta; \alpha,1)$ where $F(x / \beta; \alpha,1)$ is the standard gamma distribution cdf $$ F(x;\alpha,1) = \frac{1}{\Gamma(\alpha)}\int_0^x {y^{\alpha-1}e^{-y}} \text{d}y $$
To integrate that, it looks like I need to use the chain rule, but our professor never did an example. Is there a shortcut method? We've never used integration in a real example, only to define the pdf and get the cdf for different distributions.
Edit
The examples in my textbook involving standard gamma distribution problems say to look up the values for $F(x;\alpha)$ in Table A.4 of the appendix. When I looked, Table A.4 was missing, which really disappoints me. Are there any standard gamma distribution tables online that I can print out and hand in with the assignment? I checked Wolfram Alpha but they didn't have one. Casio has something, but I'm not sure what the shape and scale parameters are.
Edit 2
Found that table. In the front of the book, it Table A.5 came right after A.3, which is why I thought A.4 was missing. I went to the library to see if they had the same textbook; they did, and someone had the common sense (which I didn't have) to look in the back of the book, and there it was. No more help is needed.