Emails arrive at the server of a company at the rate of an average of 10 per hour. It is assumed that a Poisson process is a good model for the arrivals of the emails.

Part a)

What is the probability (to 2 decimal places) that the time between two consecutive emails is more than two minutes?



Part b)

Consider the waiting time (in minutes) for three consecutive emails to arrive. Which of the following is a plot of the density function for this random variable?







 
I   II
 
III   IV

(Click on a graph to enlarge it.)


Part c)

Find to 2 d.p. the probability that the waiting time in (b) is greater than 5 minutes.

Answer:

You can earn partial credit on this problem.