The random variable X is the number of the number of calls
received by a switchboard. Suppose X follows a Poisson
distribution and the average number of occurrences in 30 minutes
is four.
(1) What is the probability that between 10:00 and 10:30 the
switchboard will receive exactly five calls?
(2) What is the probability that between 11:00 and 11:30 the
switchboard will receive more than two calls but fewer than six
calls?
(Please show the detail computation steps. Please don’t just give
an answer from Excel functions or calculator functions. Otherwise,
you will not get all the points.)
[Hint: Please see Chapter 5 – Slides 35- 40 for Poisson
Probability Distribution. Please also see related pages in the
textbook.]