EBK FIRST COURSE IN PROBABILITY, A
10th Edition
ISBN: 9780134753683
Author: Ross
Publisher: VST
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Textbook Question
Chapter 8, Problem 8.23P
Let X be a Poisson random variable with
a. Use the Markov inequality to obtain an upper bound on
b. Use the one-sided Chebyshev inequality to obtain an upper bound on p.
c. Use the Chernoff bound to obtain an upper bound on p.
d. Approximate p by making use of the central limit theorem.
e. Determine p by running an appropriate program.
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Students have asked these similar questions
Which statements are true?
Select one or more:
a. Markov’s inequality is only useful if I am interested in that X is larger than its expectation.
b. Chebyshev’s inequality gives better bounds than Markov’s inequality.
c. Markov’s inequality is easier to use.
d. One can prove Chebyshev’s inequality using Markov’s inequality with (X−E(X))2.
Which statements are true?
Select one or more:
a. Markov's inequality is only useful if I am interested in that X is larger than its expectation.
b. Chebyshev's inequality gives better bounds than Markov's inequality.
c. Markov's inequality is easier to use.
d. One can prove Chebyshev's inequality using Markov's inequality with (X-E(X))-.
Markov’s inequality states that
Select one:
a. P(|X|≥t)≤E(X)/t for all random variables X and all t≥0.
b. P(|X|≤t)≤E(X)/t for all random variables X and all t≥0.
c. P(X≥t)≤E(X)/t for all non-negative random variables X and all t≥0.
d. P(X≤t)≤E(X)/t for all non-negative random variables X and all t≥0.
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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