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 = 0.366 for this random variable. (Round your answers to three decimal places.) What is the probability that a drought lasts exactly 3 intervals? Hint: If the drought lasts exactly 3 intervals, then the 4th interval is the first one with a surplus (a success). Our definition of the geometric random variable would be that X is the number of intervals until a success. So by our definition, P(drought lasts exactly 3 intervals)=P(X=4).
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 = 0.366 for this random variable. (Round your answers to three decimal places.)
What is the probability that a drought lasts exactly 3 intervals?
Hint: If the drought lasts exactly 3 intervals, then the 4th interval is the first one with a surplus (a success). Our definition of the geometric random variable would be that X is the number of intervals until a success. So by our definition, P(drought lasts exactly 3 intervals)=P(X=4).
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