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 = 0.374 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

(A)

proability that draught lasts exactly 3 intervals, P(X=3) = p^3*(1-p) = 0.374^3 * (1-0.374) = 0.0327

Probability that draught lasts at most 3 intervals, P(X<=3) = (1-p) + p*(1-p) + p^2*(1-p) + p^3*(1-p)

P(X<=3) = (1-0.374) + 0.374*(1-0.374) + 0.374^2*(1-0.374) + 0.374^3*(1-0.374) = 0.9804

b)

mean = 1/p = 1/0.374 = 2.6738

std. dev. = (1-p)/p^2 = (1-0.374)/0.374^2 = 4.4754

mean + std. dev. = 2.6738 + 4.4754 = 7.1492)

P(X > 7) = p^7*(1-p) = (0.374)^7*(1-0.374) = 0.00064

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---

---

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