2. Bob and Alice are dating, and all of their dates are scheduled to start at 9pm. Alice always arrives promptly at 9pm. Bob is highly disorganized and arrives at a time that is uniformly distributed between 8pm and 10pm. Let X be the time in hours between 8pm and the time when Bob arrives. If Bob arrives before 9pm, the date will last for exactly 3 hours. If Bob arrives after 9pm, their date will last for a time that is uniformly distributed between 0 and 3X hours. The date starts at the time they meet. Alice gets annoyed when Bob is late and will end the relationship after the second date on which Bob is late by more than 30 minutes. All dates are independent of any other dates. (a What is the expected number of hours Alice waits for Bob to arrive? What is the variance of the duration of any particular date? (c l (b) What is the expected duration of any particular date? ) (d) What is the expected number of dates they will have before breaking up