Question

John and Jane are working on a project, and all of their project meetings are scheduled to start at 9:00. John always arrives promptly at 9:00. Jane is highly disorganized and arrives at a time that is uniformly distributed between 8:45 and 10:28. The time (measured in minutes, a real number that can take fractional values) between 8:45 and the time Jane arrives is thus a continuous, uniformly distributed random variable.

If Jane arrives before 9:00, their project meeting will last exactly 197 minutes. If Jane arrives after 9:00, their project meeting will last for a time (measured in minutes, a real number that can take fractional values, i.e., a continuous random variable) that is uniformly distributed between 0 and 197 minutes. The meeting starts at the time they meet.

What is the expected duration of any particular project meeting?

Answer 1

SOLUTION:

GIVEN THAT