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# According to the article “Characterizing the Severity and ISBN: 9780321629111 32

## Solution for problem 78E Chapter 3

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Problem 78E

According to the article “Characterizing the Severity and Risk of Drought in the Poudre River, Colorado” (J. of Water Res. Planning and Mgmnt., 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?

Step-by-Step Solution:

Answer Step 1 of 4 Given p=0.409, q=1-0.409=0.591 The pmf of geometric distribution is P(x)=p q-1 Step 2 of 4 a) The probability that a drought lasts exactly 3 intervals P(3)=(0.409) (0.591) =0.0989

Step 3 of 4

Step 4 of 4

##### ISBN: 9780321629111

This full solution covers the following key subjects: drought, Intervals, Water, length, Probability. This expansive textbook survival guide covers 18 chapters, and 1582 solutions. The full step-by-step solution to problem: 78E from chapter: 3 was answered by , our top Statistics solution expert on 05/06/17, 06:21PM. The answer to “According to the article “Characterizing the Severity and Risk of Drought in the Poudre River, Colorado” (J. of Water Res. Planning and Mgmnt., 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?” is broken down into a number of easy to follow steps, and 117 words. Probability and Statistics for Engineers and the Scientists was written by and is associated to the ISBN: 9780321629111. Since the solution to 78E from 3 chapter was answered, more than 1314 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Probability and Statistics for Engineers and the Scientists, edition: 9.

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According to the article “Characterizing the Severity and

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