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18.440 Probability and Random Variables MIT Department of Mathematics April 25, 2007 Due: Wednesday, May 2, 2007 Problem Set 9 Problem 1 Chapter 7, #40 Problem 2 Chapter 7, #50 Problem 3 Chapter 7, #45 Problem 4 Chapter 7, #62 Problem 5 Chapter 7, #75 (Follow the hint given.) Problem 6 Chapter 7, #77 (Hint: First find the marginal density of Y and then the conditional density of X given Y . Use iterated expectation.) Problem 7 Chapter 7, Theoretical Exercise #41 1