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According to the article “Characterizing the Severity and
Chapter 4, Problem 78E(choose chapter or problem)
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?
Questions & Answers
QUESTION:
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?
ANSWER: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