For $Y$ a random variable that has sample space $S = [0, \infty)$ with a density function, $$ f\_Y (y) = 9ye^{−3y} $$

Find:

1) $P\{Y > \frac 1 3\}$

2) $\operatorname{E}\left(\frac 1 Y \right)$

---

I learned how to integrate by parts (years ago, so I'm a bit rusty) and I know there's countless resources online, but in terms of probability density functions I get a bit confused. My notes from lecture uses substitution when simplifying an integral something with gamma or E? I'm guessing this shortcut in simplifying is how to get through this problem.