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4 9496 Fri Mar 10 9:28 PM Fahd Fahd a E Chrome File Edit View History Bookmarks People Window Help Welco x Thread x VA Sectio x G An ele x c Search x c For A CE X C For A CE X C or A ce X C For A CE X C For A co x C For A CEX Fahd C www.webassign.net/ dep 15385762 web/Student/Assignment-Responses/submit? eed Help? LRead It LTalk to a tutor II 3. -13 points My Notes Ask Your Teacher For a certain river, suppose the drought length Yis the number of consecutive time intervals in which the water supply remains below a critical value yo (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 0.374 for this random variable. (Round your answers to three decimal places.) (a) What is the probability that a drought lasts exactly 3 intervals? ply exceeds the critical level during the 4th time interval.) At most 3 intervals? 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? Submit Answer Save Progress Practice Another Version Submit Assignment Save Assignment Progress Home My Assignments Extension Request' WebAssign 4.0 1997-2017 Advanced Instructional Systems, Inc. All rights reserved. Show All SCANO667 JPG

Explanation / Answer

a) P(X=3) =(1-0.374)3*0.374 =0.0917

2)P(X<=3) =1-(1-0.374)3 =1-0.2453 =0.7547

b) mean =1/0.374 =2.674

std deviation =((1-p)/p2)1/2 =4.475

mean +std deviation =7.149

hence P(X>=8) =(1-0.374)7 =0.0377

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