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 8:25 and 10:35. The time (measured in minutes, a real number that can take fractional values) between 8:25 and the time Jane arrives is thus a continuous, uniformly distributed random variable.

What is the expected duration of time (measured in minutes, a real number that can take fractional values) John waits for Jane to arrive?

Answer 1

Hello

YOUR REQUIRED ANSWER IS 30 minutes

Given that Jane arrives between 8:25 and 10:35, which means that she arrives in a duration of 130 min(35min+60min+35min).

Hence, her arrival is uniformaly distributed over this period of 130 minutes.

Now, as John arrives at exact 9 AM, hence, we have to calculate the expected duration of time John has to wait.

Now,

Expected time of arrival of Jane = 8:25 + (130/2) = 8:25 + 65 minutes = 9:30 AM

Hence, expected time John has to wait = 30 minutes(9:30-9:00)

Thanks!

Please drop an upvote if you find this helpful.