For a certain river suppose the drought length the number of

For a certain river, suppose the drought length the number of consecutive time intervals in which the water supply remains below a critical value yo a deficit , preceded by and followed by penods in which the supply e ceeds this crtical value a surplus An article proposes a geometric distribution with -0371 for this random variable. Round your answers to three dedmal paces.) (a) What is the probability that a drought lasts exactly 3 intervals? At most 3 intervals? exactly 3 intervals 0321x at most 3 intervals 9807X What is the probablity that the length of a drought exceeds its mean value by at least one standard deviation? . x 00001

Solution

a)drought lasts exactly 3 intervals=P(till 2 interval did not and last in 3rd) =(1-0.371)²*0.371=0.147

at most 3 intervals =1-P( did not last till 3rd interval) =1-(1-0.371)³ =0.751

b)here mean =1/p=2.695 and std deviation =((1-p)/p²)^1/2 =2.137

therefore above 1 std deviation from mean =>=5

hence probability that length exceeds one std deviation from mean =P(X>=5) =(1-0.371)⁴=0.157