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 8:20 and 10:50. The time (measured in minutes, a real number that can take fractional values) between 8:20 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 175 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 175 minutes. The meeting starts at the time they meet.

What is the expected duration of any particular project meeting?

Answer 1

Solution:-

Given that

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 8:20 and 10:50. The time (measured in minutes, a real number that can take fractional values) between 8:20 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 175 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 175 minutes. The meeting starts at the time they meet.

What is the expected duration of any particular project meeting?

The expected duration of an particular project meeting will depend on the Jane's time of arrival.

pdf of Jane's time of arrival =

=

Now, the probability that Jane will arrive before 9:00

The probability that the meeting will last 175 min =

Now, the probability that Jane will arrive after 9:00

  

  

Expected duration of meeting if Jane arrives after 9:00

  

= 87.5

So, Total expected duration of any project meeting

  

  

   

  

Thanks for supporting...

Please give positive rating...