According to the article \"Characterizing the Severity and Risk of Drought in th

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 (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 0.1 for this random variable. What is the probability that the length of a drought exceeds its mean value? 15 pts]

Explanation / Answer

Y follow geometric distribution with p = 0.1

P(Y > mean(Y))

Y can take 0,1,2..

E(Y) = (1-p)/p = 0.9/0.1 = 9

P(Y > 9)

= 1- P(Y <= 8)

=1 - (1-p)^(8+1)

=1 - 0.9^9

= 0.612579

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