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 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 = 0.362 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?

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

exactly 3 intervals     at most 3 intervals    

Explanation / Answer

geometric distribution

p = 0.362

P(X = k) = (1 -p)^(k) p

P(X = 3) = ( 1 - 0.362)^3 * 0.362

= 0.0940092

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

= 0.834315

0 0.362 1 0.230956 2 0.14735 3 0.094009 total 0.834315

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