324.sample.final - Stat324 Sample Final Exam Moo K Chung...

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Stat324: Sample Final ExamMoo K. Chung[email protected]May 5, 20051. Suppose thatX1,· · ·, Xnis a random sample from the Bernoulli distribution withP(Xi= 1) =p,0< p <1(20pts)(a) Compute the correlation coefficient ofX1+X2andX1+X3.(b) Determine the probability distribution ofX21+· · ·+X2n.
2. The density ofXis given byf(x) =|x|for-1< x <1andf(x) = 0otherwise (20pts).(a) Compute the cumulative distribution ofXand plot its graph.(b) Determine the density ofU=X21+x2
(3. Gross sales before and after a training program is given bySalesperson : 1 23 45 6Sales before: 90 83 105 97 110 78Sales after : 97 80 110 93 123 84Determine if the training program is effective atα= 0.1. Carefully do your analysis stating all the relevant assumptions(30 pts).

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