$\frac{2}{b-a}$
The PDF of the above function $f_x(x)$ is:
$f_x(x) = \begin{cases} \frac{2(x-a)}{(b-a)(m-a)}, & \text{if } a \le x < m\\ \frac{2(b-x)}{(b-a)(b-m)}, & \text{if } m \le x \le b \end{cases}$
The CDF of the above function $F_x(x)$ is:
$F_x(x) = \begin{cases} 0, & \text{if } x < a\\ \frac{(x-a)^2}{(b-a)(m-a)}, & \text{if } a \le x < m\\ 1 - \frac{(b-x)^2}{(b-a)(b-m)}, & \text{if } m \le x < b\\ 1, & \text{if } x \ge b \end{cases}$
Suppose Cost is a continuous random variable whose possible values are given by the interval $15 \le x \le 75$, where $x$ is in dollars million ($M$), with mode $m = 40$.
a. Substitute in the values and write down the PDF of Cost.
b. Substitute in the values and write down the CDF of Cost.
c. Compute $P(Cost \le 30)$.
d. Compute $P(30 < Cost < 70)$.
e. Compute $P(Cost > 75)$.
f. Determine a value $x$ such that $P(Cost \le x) = 0.80$.
