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ps10 - University of Illinois Spring 2010 ECE 313 Problem...

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University of Illinois Spring 2010 ECE 313: Problem Set 10 Due: Wednesday, April 7 at 4 p.m. Reading: Ross, Chapter 5; Lecture Notes 26-28. Noncredit Exercises: DO NOT turn these in. Chapter 5: Problems 11,15 and 31; Theoretical Exercises 18,30. This Problem Set contains seven problems. 1. [Moments of random variables] Theoretical Exercises, Chapter 5 of the textbook, Problem 5.5. 2. [Gaussian Random Variables] Let X be a Gaussian random variable with mean μ = - 1 and variance σ 2 = 4. (a) Find the mean and variance of 2 X + 5. Let Φ( x ) denote the CDF of a standard Gaussian random variable, and let Q ( x ) = 1 - Φ( x ). Suppose that Calculator A can evaluate only Φ( x ) and only for nonnegative values of x . On the other hand, suppose that Calculator B can evaluate only Q ( x ), again only for x 0. Both calculators can perform standard functions, like addition and multiplication. For each of the probabilities in parts ( b ) through ( e ), write down two alternative expressions: one for evaluation using Calculator A, and the other for
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