# If we assume the counter starts in the unlocked state

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Unformatted text preview: follows a Poisson process with rate 4. Suppose that 3/4’s of the calls are made by men, 1/4 by women, and the sex of the caller is independent of the time of the call. (a) What is the probability that in one hour exactly 2 men and 3 women will call the answering service? (b) What is the probability 3 men will make phone calls before 3 women do? 2.61. Hockey teams 1 and 2 score goals at times of Poisson processes with rates 1 and 2. Suppose that N1 (0) = 3 and N2 (0) = 1. (a) What is the probability that N1 (t) will reach 5 before N2 (t) does? (b) Answer part (a) for Poisson processes with rates 1 and 2 . 2.62. Consider two independent Poisson processes N1 (t) and N2 (t) with rates 1 and 2 . What is the probability that the two-dimensional process (N1 (t), N2 (t)) ever visits the point (i, j )? 100 CHAPTER 2. POISSON PROCESSES Chapter 3 Renewal Processes 3.1 Laws of Large Numbers In the Poisson process the times between successive arrivals are independent and exponentially distributed. The lack of mem...
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## This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).

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