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It is your birthday and you are waiting for someone to write you a birthday message on Facebook. On average (on your birthday) you receive a facebook message every 10 minutes. Assume that the times between the birthday messages are independent.
a) What is the probability the next posting takes 15 minutes or longer to appear?
b) What is the standard deviation of the time between birthday postings?
c) What is the probability that it takes 12.5 minutes for the next birthday posting?
d) Suppose that the most recent birthday posting was done at 1:40 pm and it is now 1:45 pm. What is the probability that you will have to wait until 1:53 pm or later for the next message?
e) What is your median waiting time for birthday messages?
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