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 y (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 p0.388 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? Need Help? ReadIt Taik to a Tutor

Explanation / Answer

a)

P(X = x) = q^x * p

P(X = 3) = (1 - 0.388)^3 * 0.388

= 0.08893

at most 3 interval

P(X <= 3) = P(X = 0) + P(X = 1) +P(X = 2) +P(X = 3)

= 0.388 + 0.612 * 0.388 + 0.612^2 * 0.388 + 0.08893

=0.859709072

b)

mean = (1- p)/p = 0.612/0.388 = 1.5773195

sd = sqrt( (1-p)/p^2) = sqrt(0.612/0.388^2) = 2.016248

P(X > 1.577 + 2.016)

= P(X > 3.593)

= P(X >=4)

= 1 - P(X <= 3)

= 1 - 0.8597090

=0.140291

Please rate

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---

---

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