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 = 0.369 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?

If you could please justify your steps, that would be appreciated! I want to be able to learn the material :)

Thanks in advance!

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 = 0.369 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?

If you could please justify your steps, that would be appreciated! I want to be able to learn the material :)

Thanks in advance!