Chapter 15.4, Problem 32E

Xavier and Yolanda both have classes that end at noon and they agree to meet every day after class. They arrive at the coffee shop independently. Xavier’s arrival time is X and Yolanda’s arrival time is Y, where X and Y are measured in minutes after noon. The individual density functions are $f_1(x)=\{\begin{array}{cc}{e}^{-x}& ifx\ge 0\\ 0& ifx<0\end{array}{f}_2(y)=\{\begin{array}{cc}\frac{1}{50}y& \text{if}\text{0}\le \text{y}\le \text{10}\\ 0& \text{otherwise}\end{array}$

(Xavier arrives sometime after noon and is more likely to arrive promptly than late. Yolanda always arrives by 12:10 pm and is more likely to arrive late than promptly.) After Yolanda arrives, she’ll wait for up to half an hour for Xavier, but he won’t wait for her. Find the probability that they meet.