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hw6 - AMS 311(Fall 2009 Joe Mitchell PROBABILITY THEORY...

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AMS 311 (Fall, 2009) Joe Mitchell PROBABILITY THEORY Homework Set # 6 Due at the beginning of class on Thursday, November 5, 2009. Reminder: Show your reasoning! You do not need to evaluate arithmetic expressions or integrals, if they are fully specified. For example, you may leave integraltext 0 . 5 0 integraltext 1 - x x x 2 e y dydx in this form. Read: Ross, Chapter 6 (Sections 6.1, 6.2); Handouts: (1) Continuous Distributions; (2) Expectation, Moment Generating Functions, Variance, and Covariance. (1). (20 points) [See related problems 39-41, Ross (Chap 6). See Examples 1a, 1b.] Suppose that X and Y have joint mass function as shown in the table below. (Here, X takes on possible values in the set {- 2 , 1 , 3 } , Y takes on values in the set {- 2 , 0 , 1 , 3 . 1 } .) -2 0 1 3.1 -2 .1 .2 0 0 1 .1 0 .4 0 3 0 .1 0 .1 (a). (7 points) Compute P ( | X 2 - Y | > 0). (b). (7 points) Find the marginal mass function of X and plot it. (be very explicit!) (c). (6 points) Compute var ( X 2 ) (2). (20 points) Joe and Estie plan to study together for the AMS311 test. They decide to meet at the library between 8:00pm and 8:30pm. Assume that they each arrive at a random time in this interval. What is the probability that
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