For a certain river, suppose 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). An article proposes a geometric distribution with p = 0.397 for this random variable. (Round your answers to three decimal places.) ***Please explain the steps and show what formula is being used.*** (a) What is the probability that a drought lasts exactly 3 intervals? (b) At most 3 intervals? (c) What is the probability that the length of a drought exceeds its mean value by at least one standard deviation?

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For a certain river, suppose 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). An article proposes a geometric distribution with p = 0.397 for this random variable. (Round your answers to three decimal places.)

***Please explain the steps and show what formula is being used.***

(a) What is the probability that a drought lasts exactly 3 intervals?

(b) At most 3 intervals?

(c) What is the probability that the length of a drought exceeds its mean value by at least one standard deviation?

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