A company is preparing to launch a new web site to sell its products. From past experience, they know that purchases at the site will occur as a Poisson process with on average 30 purchases every 10 minutes.
a) What is the expected time in minutes before the first purchase after the site opens? Give your answer to four decimal places.
b) What is the probability that more than 0.14 minutes pass before the first purchase? Give your answer to four decimal places.
c) What is the expected time in minutes until the fifth purchase? Give your answer to four decimal places.
Poisson process is a formula for a series of event where the interval between events is provided but the exact timing is random and the arrival of an event is independent on previous event.
