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Unformatted text preview: AMS 311 (Fall, 2010) Joe Mitchell PROBABILITY THEORY Homework Set # 6 Due at the beginning of class on Thursday, November 4, 2010. 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 . 5 integraltext 1- x x x 2 e y dydx in this form. Ross, Chapter 6 (Sections 6.1, 6.2); Read: Handout on Expectation, Moment Generating Functions, Variance, and Covariance. (1). (20 points) Two fair dice are rolled. Find the joint probability mass function of X and Y , where X is the larger of the two values and and Y is the smaller of the two values on the dice. (e.g., if the roll is (4,2), then X = 4 and Y = 2, while if the roll is (4,4), then X = Y = 4) (2). (25 points) Let X and Y be independent exponential random variables with respective parameters 2 and 3. Find the cdf and density of Z = X/Y . Also, compute P ( X &lt; Y )....
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- Spring '08