The time, in minutes, it takes to reboot a certain system is a continuous variable with the density:
$f(x) = \begin{cases} C(10-x)^2 & \text{if }0 < x < 10 \\ 0 & \text{otherwise}\end{cases}$
- Compute $C$
- Compute the probability that it takes between 1 and 2 minutes to reboot.
For part 2 I believe I should take the integral of $f(x)$ from $1$ to $2$ but for part 1 I am not sure.
Though answers do help, I'm looking for more of a how to then the solutions so I can do this on my own for the test.