timne ietervals in which the water supply remains below a critical vakue yo (a d

Question

timne ietervals in which the water supply remains below a critical vakue yo (a deficit). preceded by follied by periods in which the supply exceeds this oritical vaue (a surphus).An article proposes a geometric distribution with p-0409 for this to three decimal places) (a) what is the protability that a drought lasts exactly 3 intervalisr (Supply exceeds the aritical evel during the 4th time interval.) At most 3 intervals? exactly 3 intervals 0064 at most 3 intervals 3704 )what is tho probabity that the lenyh of a drought exconds its mean vah" by at inast one standard deviation

Explanation / Answer

Solution-

P(drought lasts for 3 times) = p * p * p

= 0.409 * 0.409 * 0.409

= 0.0684

P(drought lasts for atmost 3 times) = P(drought lasts for 3 times) + P(drought lasts for 2 times)+ P(drought lasts for 1 time) + P(no drought occurr)

= p * p * p + p * p * (1-p) + p * (1-p) * (1-p) + *(1-p) * (1-p) * (1-p)

= 0.409 * 0.409 * 0.409 + 0.409 * 0.409 * 0.591 + 0.409 * 0.591 * 0.591 + 0.591 * 0.591 * 0.591

= 0.5166

(b) standard deviation = [0.409*0.591]^0.5

= 0.4916

mean = 0.409

So mean + standard deviation = 0.409 + 0.4916 = 0.90065

hence required probability = P(drought lasts for more than or equal a year)

= 1 - P(no drought)

= 0.591

Answer

TY!

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