It is your birthday and you are waiting for someone to write a "Happy Birthday" message on your Face book wall. Your waiting lime is approximately Exponential with average waiting time of 10 minutes between such postings; assume that the times of the postings are independent.
a. What is the probability that the next posting takes 15 minutes or longer to appear?
b. What is the standard deviation of the time in between consecutive Happy Birthday messages?
c. Suppose that the most recent posting was done at 1:40 PM, and it is now 1:45 PM (i.e., no postings have been made during the last five minutes). What is the expected time for the next message to appear?