EBK FIRST COURSE IN PROBABILITY, A
10th Edition
ISBN: 9780134753676
Author: Ross
Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)
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Chapter 8, Problem 8.12P
We have 100 components that we will put in use in a sequential fashion. That is, component 1 is initially put in use, and upon failure, it is replaced by component 2, which is itself replaced upon failure by component 3, and so on. If the lifetime of component i Is exponentially distributed with
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CD4 cells are carried in the blood as part of the human immune system. One of the effects of the HIV virus is that these cells die. In this study of the effectiveness of a new anti-viral drug on HIV, 20 HIV-positive patients had their CD4 counts recorded (“Baseline”) and then were put on a course of treatment with this drug. After using the drug for one year, their CD4 counts were again recorded (“OneYear”). The aim was to show that patients taking the drug had increased CD4 counts which is not generally seen in HIV-positive patients.
Baseline
OneYear
2.12
2.47
4.35
4.61
3.39
5.26
2.51
3.02
4.04
6.36
5.1
5.93
3.77
3.93
3.35
4.09
4.1
4.88
3.35
3.81
4.15
4.74
3.56
3.29
3.39
5.55
1.88
2.82
2.56
4.23
2.96
3.23
2.49
2.56
3.03
4.31
2.66
4.37
3.00
2.40
1) What is the correlation between baseline and one year CD4 counts?
In a printing shop, print requests arrive randomly and independently at anaverage rate of 20 per hour and are placed in a queue according to arrival times.Suppose that the time it takes to process each request is exponentiallydistributed and that the print times for different jobs are independent.A particular printer in this shop is capable of printing five pages perminute. The average request results in ten printed pages of poster.
(i)There are currently five jobs in the queue – one active and fourwaiting to be processed. A new customer submit a job to this printerand it becomes the sixth job in the queue. Calculate the probabilitythat he will have to wait more than 5 minutes for the printer tobegin processing his job. Assume that the time between consecutivejobs in the queue is negligible.(ii) Name the alternative distribution of the random variable that youare considering in (i)
Chapter 8 Solutions
EBK FIRST COURSE IN PROBABILITY, A
Ch. 8 - Suppose that X is a random variable with mean and...Ch. 8 - From past experience, a professor knows that the...Ch. 8 - Use the central limit theorem to solve part (c) of...Ch. 8 - Let X1,...,X20 be independent Poisson random...Ch. 8 - Fifty numbers are rounded off to the nearest...Ch. 8 - A die is continually rolled until the total sum of...Ch. 8 - A person has 100 light bulbs whose lifetimes are...Ch. 8 - In Problem 8.7, suppose that it takes a random...Ch. 8 - If X is a gamma random variable with parameters...Ch. 8 - Civil engineers believe that W, the amount of...
Ch. 8 - Many people believe that the daily change of price...Ch. 8 - We have 100 components that we will put in use in...Ch. 8 - Student scores on exams given by a certain...Ch. 8 - A certain component is critical to the operation...Ch. 8 - An insurance company has 10.000 automobile...Ch. 8 - A.J. has 20 jobs that she must do in sequence,...Ch. 8 - Redo Example 5b under the assumption that the...Ch. 8 - Repeat part (a) of Problem 8.2 when it is known...Ch. 8 - A lake contains 4 distinct types of fish. Suppose...Ch. 8 - If X is a nonne9ative random variable with mean...Ch. 8 - Let X be a nonnegative random variable. Prove that...Ch. 8 - Prob. 8.22PCh. 8 - Let X be a Poisson random variable with mean 20....Ch. 8 - Prob. 8.24PCh. 8 - Prob. 8.25PCh. 8 - If f(x) is an Increasing and g(x) is a decreasing...Ch. 8 - If L(p) is the Lorenz curve associated with the...Ch. 8 - Suppose that L(p) is the Lorenz curve associated...Ch. 8 - If X has variance 2, then , the positive square...Ch. 8 - If X has mean and standard deviation , the ratio...Ch. 8 - Compute the measurement signal-to-noise ratio-that...Ch. 8 - Let Zn,n1, be a sequence of random variables and...Ch. 8 - Prob. 8.5TECh. 8 - Prob. 8.6TECh. 8 - Prob. 8.7TECh. 8 - Explain why a gamma random variable with...Ch. 8 - Prob. 8.9TECh. 8 - If X is a Poisson random variable with mean , show...Ch. 8 - Prob. 8.11TECh. 8 - Prob. 8.12TECh. 8 - Prob. 8.13TECh. 8 - Prob. 8.14TECh. 8 - If f and g are density functions that are positive...Ch. 8 - Prob. 8.16TECh. 8 - The number of automobiles sold weekly at a certain...Ch. 8 - Prob. 8.2STPECh. 8 - If E[X]=75E[Y]=75Var(X)=10var(Y)=12cov(X,Y)=3 give...Ch. 8 - Prob. 8.4STPECh. 8 - Prob. 8.5STPECh. 8 - Prob. 8.6STPECh. 8 - Prob. 8.7STPECh. 8 - Prob. 8.8STPECh. 8 - Prob. 8.9STPECh. 8 - A tobacco company claims that the amount of...Ch. 8 - Prob. 8.11STPECh. 8 - Prob. 8.12STPECh. 8 - The strong law of large numbers states that with...Ch. 8 - Each new book donated to a library must be...Ch. 8 - Prove Chebyshevs sum inequality, which says that...
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