The storm runoff $x($in cubic meters per second, cms$)$ from a subdivision can be modeled by a random

variable with the following PDF:

$f_x(x)=\{\begin{array}{ccc}\frac{1}{6}(x-\frac{x^2}{6})& \text{f}\text{o}\text{r}& 0x6\\ 0& \text{o}\text{t}\text{h}\text{e}\text{r}\text{w}\text{i}\text{s}\text{e}& \end{array}$

a$)$ Compute the CDF of $x$

b$)$ The runoff is carried by a pipe with a capacity of $4$ cms $.$ Overflow will occur when the runoff exceeds the

pipe capacity. What is the probability of overflow?

c$)$ If overflow occurs after a storm, what is the probability that the runoff in this storm is less than $5$ cms $?$

$($Hint: recall lecture $1,$ notion of conditioning events...$)$