Refer to Exercise 2.
a. Find the probability that there will be exactly 5 requests in a 2-second time interval.
b. Find the probability that there will be more than 1 request in a 1.5-second time interval.
c. Find the probability that there will be no requests in a 1-second time interval.
d. Find the probability that the time between requests is greater than 1 second.
e. Find the probability that the time between requests is between 1 and 2 seconds.
f. If there have been no requests for the past two seconds, what is the probability that more than one additional second will elapse before the next request?
(a) The mean time between requests is 0.5 s, so the mean number of requests is two per second. Let X be the number of requests in two seconds. It follows that X ~ Poisson(4).
(b)Let X be the number of requests in a 1.5 second time interval. Then X ~ Poisson(3).
(c) Let X be the number of requests in a 1 second time interval. Then X ~ Poisson(2).
(d) Let Tbe the time between requests. Then 
(e) Let Tbe the time between requests. Then
(f)
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