For a certain river, suppose the drought length Y is the number of consecutive t

Question

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 yo (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 0.375 for this random variable. (Round your answers to three decimal places.) (a) What is the probability that a drought lasts exactly 3 intervals? At most 3 intervals? 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?

Explanation / Answer

Y - geometric distribution with p = 0.375

a)

P(Y = 3) = 0.146484

P(Y<= 3) =0.755859

b)

mean = 2.666666

sd = 2.108185

mean + sd = 2.666666 + 2.108185 = 4.774851

P(X > 4.774851) =

P(X>=5) = 0.152587

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.