324.final.2005 - STAT-324 Final Exam 12:25-2:25AM...

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STAT-324Final ExamMay 11, 200512:25-2:25AMInstructor: Moo K. ChungAnswer all questions showing all your work neatly.Calculators are allowed. One page note is permittedName:Student ID:Pledge: On my honor, I have neither given nor receivedunauthorized aid on this examination.Signature:QuestionPoints12345Total
You may use the followingRoutput for the answering exam problems.> qnorm(c(0.005,0.01,0.025,0.05,0.1))[1] -2.575829 -2.326348 -1.959964 -1.644854 -1.281552> qt(0.025,5:11)[1] -2.57 -2.44 -2.36 -2.30 -2.26 -2.22 -2.20> qt(0.05,5:11)[1] -2.01 -1.94 -1.89 -1.85 -1.83 -1.81 -1.79> qt(0.01,5:11)[1] -3.36 -3.14 -2.99 -2.89 -2.82 -2.76 -2.71> qf(0.025,1,5:11)[1] 0.001084778 0.001067109 0.001054611 0.001045308 0.0010381150.001032389 [7] 0.001027723> qf(0.05,1,5:11)[1] 0.004344768 0.004273760 0.004223537 0.004186155 0.0041572560.004134252 [7] 0.004115506> qf(0.01,1,5:11)[1] 0.0001735012 0.0001706780 0.0001686808 0.0001671942 0.0001660447[6] 0.0001651297 0.00016438401. Two playersAandBflip a biased coin alternately and the first player to obtain a head wins.The probability of obtaining a head isp >0 at each toss. SupposeAflips the coin first.(a) Find the probability thatAwins the game. Derive your result [10pts].

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