11ProbHw9 - IEOR 3658 Probability Prof. Mariana...

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IEOR 3658 Assignment #9 Probability November 9, 2011 Prof. Mariana Olvera-Cravioto Page 1 of 2 Assignment #9 – due November 16th, 2011 1. Let X and Y be independent exponentially distributed random variables with parameters λ and μ , respectively. (a) Compute the PDF of S = min { X,Y } . Does it look like a familiar distribution? ( Hint: Compute 1 - F S ( s ) first.) (b) Compute P ( X Y ). 2. X and Y are two independent random variables, each of which is uniformly distributed between zero and one. Let A be the event: min( X,Y ) < 0 . 5. (a) Compute the joint density of X and Y given A . Are X and Y independent given event A ? (b) Let W = XY . Compute the conditional expectation of W given event A , i.e., E [ W | A ]. ( Hint: work directly on the ( x,y ) - plane.) (c) Let Z = max( X,Y ) and define the event B = { Z < 0 . 75 } . Compute the conditional probability of B given A , that is, P ( B | A ). 3. The joint PDF of
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11ProbHw9 - IEOR 3658 Probability Prof. Mariana...

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