EBK FIRST COURSE IN PROBABILITY, A
10th Edition
ISBN: 9780134753676
Author: Ross
Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)
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Chapter 10, Problem 10.3STPE
To determine
To calculate: an efficient algorithm to stimulate a random variable having probability mass
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In a small office, there are m = 5 typists who need to use a single typewriter to complete their reports. Assume the time
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averaging 30 minutes to complete a report (μ 2 reports/hour). Given that the number of typists is finite and all typists
=
share one typewriter, they will form a waiting queue.
(1). Describe this queuing system and explain how it fits the characteristics of the M/M/1/∞0/m model.
(2). Calculate the probability that any typist is using the typewriter at steady-state.
(3). Calculate the average number of typists waiting in the queue at steady-state.
(4). Considering the need to reduce waiting time, if an additional typewriter is introduced (turning into a two-server
system, or M/M/2/∞0/m model), analyze the expected impact,…
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Theorem 2.4 (The Hölder inequality)
Let p+q=1. If E|X|P < ∞ and E|Y| < ∞, then
.
EXY SEXY ≤ Xp Yq.
Chapter 10 Solutions
EBK FIRST COURSE IN PROBABILITY, A
Ch. 10 - The following algorithm will generate a random...Ch. 10 - Prob. 10.2PCh. 10 - Give a technique for simulating a random variable...Ch. 10 - Present a method for simulating a random variable...Ch. 10 - Use the inverse transformation method to present...Ch. 10 - Give a method for simulating a random variable...Ch. 10 - Let F be the distribution functionF(x)=xn0x1 a....Ch. 10 - Prob. 10.8PCh. 10 - Suppose we have a method for simulating random...Ch. 10 - Prob. 10.10P
Ch. 10 - Use the rejection method with g(x)=1,0x1, to...Ch. 10 - Prob. 10.12PCh. 10 - Prob. 10.13PCh. 10 - Prob. 10.14PCh. 10 - Prob. 10.15PCh. 10 - Let X be a random variable on (0, 1) whose density...Ch. 10 - Prob. 10.1STPECh. 10 - Prob. 10.2STPECh. 10 - Prob. 10.3STPECh. 10 - If X is a normal random variable with mean and...Ch. 10 - Prob. 10.5STPE
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