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 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