Example 3.2. Piecewise Constant PDF. Alvin's driving time to work is between 15 and 20 minutes if the day is sunny, and between 20 and 25 minutes if the day is rainy, with all times being equally likely in each case. Assume that a day is sunny with probability $2 / 3$ and rainy with probability $1 / 3$. What is the PDF of the driving time, viewed as a random variable $X$ ? $$ f x(x)=\left\{\begin{array}{11} c_{1}, & \text { if } 15 \leq x