# 4. (Lecture 25, Continuous Time Random Process, 9 pts) Suppose that the total number of requests...

###### Question:

4. (Lecture 25, Continuous Time Random Process, 9 pts) Suppose that the total number of requests to a web server received between time 0 and time t, N(t), is given by a Poisson random process with rate 2- 10 requests per minute (a) Find the probability that exactly 8 requests are received in the first 30 seconds. (b) Find the probability that exactly 8 requests are received in the first 30 seconds and that exactly 8 requests are received in the next 30 seconds. (c) Find the probability that the first request occurs before -3 seconds. (d) Find the probability that the first request occurs between 1-1 and 1-3 seconds. (e) Find the probability that the second request occurs before -6 seconds.

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