Explanation Let Y is an exponential random variable and the probability density function is as follows: f ( y ) = { 1 β e − y β , y > 0 0 , elsewhere The mean and standard deviation of Y is as follows: μ = β σ 2 = β 2 The P ( | Y − μ | ≤ 2 σ ) value can be obtained as follows: P ( | Y − μ | ≤ 2 σ ) = P ( | Y − β | ≤ 2 β ) = P (

Mathematical Statistics with Applications

7th Edition

ISBN: 9780495110811

Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer

Publisher: Cengage Learning

See similar textbooks

Question

Chapter 4.10, Problem 150E

To determine

Find P(|Y−μ|≤2σ) for the exponential random variable.

Compare with the corresponding probabilistic statement given by Tchebysheff’s theorem and the empirical rule.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.10, Problem 149E

Chapter 4.10, Problem 151E

Students have asked these similar questions

a small pond contains eight catfish and six bluegill. If seven fish are caught at random, what is the probability that exactly five catfish have been caught?

23 The line graph in the following figure shows Revenue ($ millions) one company's revenues over time. Explain why this graph is misleading and what you can do to fix the problem. 700 60- 50- 40 30 Line Graph of Revenue 20- 101 1950 1970 1975 1980 1985 Year 1990 2000

d of the 20 respectively. Interpret the shape, center and spread of the following box plot. 14 13 12 11 10 6 T 89 7 9 5. 治

Chapter 4 Solutions

Mathematical Statistics with Applications

Ch. 4.2 - Prob. 1E Ch. 4.2 - A box contains five keys, only one of which will...Ch. 4.2 - A Bernoulli random variable is one that assumes...Ch. 4.2 - Let Y be a binomial random variable with n = 1 and...Ch. 4.2 - Suppose that Y is a random variable that takes on...Ch. 4.2 - Consider a random variable with a geometric...Ch. 4.2 - Let Y be a binomial random variable with n=10 and...Ch. 4.2 - Prob. 8E Ch. 4.2 - A random variable Y has the following distribution...Ch. 4.2 - Refer to the density function given in Exercise...

Knowledge Booster

Find P ( | Y − μ | ≤ 2 σ ) for the exponential random variable. Compare with the corresponding probabilistic statement given by Tchebysheff’s theorem and the empirical rule .

Solution Summary: The author compares Tchebysheff's theorem and the empirical rule for the exponential random variable Y.

Find P(|Y−μ|≤2σ) for the exponential random variable.

Compare with the corresponding probabilistic statement given by Tchebysheff’s theorem and the empirical rule.

Want to see the full answer?

Chapter 4 Solutions

Find P ( | Y − μ | ≤ 2 σ ) for the exponential random variable. Compare with the corresponding probabilistic statement given by Tchebysheff’s theorem and the empirical rule .

Solution Summary: The author compares Tchebysheff's theorem and the empirical rule for the exponential random variable Y.

Find P(|Y−μ|≤2σ) for the exponential random variable. Compare with the corresponding probabilistic statement given by Tchebysheff’s theorem and the empirical rule.

Want to see the full answer?

Chapter 4 Solutions

Find P(|Y−μ|≤2σ) for the exponential random variable.

Compare with the corresponding probabilistic statement given by Tchebysheff’s theorem and the empirical rule.