Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Chapter 3.5, Problem 78E
According to the article “Characterizing the Severity and Risk of Drought in the Poudre River, Colorado” (J. of Water Res. Planning and Algmnt., 2005: 383-393), the drought length Y is the number of consecutive time intervals in which the water supply remains below a critical value y0 (a deficit), preceded by and followed by periods in which the supply exceeds this critical value (a surplus). The cited paper proposes a geometric distribution with p = .409 for this random variable.
- a. What is the
probability that a drought lasts exactly 3 intervals? At most 3 intervals? - b. What is the probability that the length of a drought exceeds its
mean value by at least one standard deviation?
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A researcher hypothesizes that in a certain country the net annual growth of private sector purchases of government bonds, B, is positively related to the nominal rate of interest on the bonds, NI, and negatively related to the rate of inflation Π:
Bt = a0 + a1NIt + a2Π t + ut
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Using a sample of 56 annual observations, s/he estimates the following equations:
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Find the maximum likelihood estimator for θ in the pdf f(y; θ) = 2y/(1 − θ^2), θ ≤ y ≤ 1.
Chapter 3 Solutions
Probability and Statistics for Engineering and the Sciences
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