Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Chapter 4.4, Problem 66E
The two-parameter gamma distribution can be generalized by introducing a third parameter g, called a threshold or location parameter: replace x in (4.8) by x − γ and x ≥ 0 by x ≥ γ. This amounts to shifting the density curves in Figure 4.27 so that they begin their ascent or descent at g rather than 0. The article “Bivariate Flood Frequency Analysis with Historical Information Based on Copulas” (J. of Hydrologic Engr., 2013:1018–1030) employs this distribution to model X = 3-day flood volume (108 m3). Suppose that values of the parameters are α = 12, β = 7, γ = 40 (very close to estimates in the cited article based on past data)
a. What are the
b. What is the
c. What is the probability that flood volume exceeds its mean value by more than one standard deviation?
d. What is the 95th percentile of the flood volume distribution?
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1) Write the null hypothesis and the alternative hypothesis (for the factor).
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3) What is your decision about the null hypothesis, consider ?.
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Chapter 4 Solutions
Probability and Statistics for Engineering and the Sciences
Ch. 4.1 - The current in a certain circuit as measured by an...Ch. 4.1 - Suppose the reaction temperature X (in C) in a...Ch. 4.1 - The error involved in making a certain measurement...Ch. 4.1 - Let X denote the vibratory stress (psi) on a wind...Ch. 4.1 - A college professor never finishes his lecture...Ch. 4.1 - The actual tracking weight of a stereo cartridge...Ch. 4.1 - The article Second Moment Reliability Evaluation...Ch. 4.1 - Prob. 8ECh. 4.1 - Based on an analysis of sample data, the article...Ch. 4.1 - A family of pdfs that has been used to approximate...
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