# PS14 - University of Illinois Fall 2009 ECE 313 Problem Set...

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University of Illinois Fall 2009 ECE 313: Problem Set 14 Conditional Distributions; Covariance and Correlation Due: Wednesday December 9 at 4 p.m. Reading: Ross, Chapter 7, Sections 1-5; Chapter 8, Sections 1-4 Powerpoint Lecture Slides, Sets 35-38 Noncredit exercises: Ross Chapter 7: Problems 1, 16, 26, 30 33, 34, 38; Theoretical Exercises: 1, 2, 17, 22, 23, 40 Chapter 8: problems 1-9, 15. Reminder: Due date for homework is Wednesdays at 4 p.m. again 1. [Is gambling any good?] John is vacationing in Monte Carlo. Each evening the amount of money he takes to the casino is a random variable X with pdf f X ( u ) = Cu 0 < u \$100 0 else . At the end of each night, the amount Y he returns with is uniformly distributed between 0 and twice the amount he came to the casino with. (a) Find the value of the constant C . (b) For fixed α , 0 α \$100, what is f Y | X ( v | α ), the conditional pdf of Y given that X = α ? (c) If John goes to the casino with α dollars, what is the probability that he returns home with more than α dollars?

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