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ps06 - University of Illinois Spring 2010 ECE 313 Problem...

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University of Illinois Spring 2010 ECE 313: Problem Set 6 Due: Wednesday, March 3rd at 4 p.m. Reading: Ross, Chapter 3; Lecture Notes 14-18. Noncredit Exercises: DO NOT turn these in. Chapter 3: Problems 80,84 and 86; Theoretical Exercises 8,16 and 21. This Problem Set contains seven problems. 1. [Conditional Probability] Die A has four red and two white faces, whereas die B has two red and four white faces. A fair coin is flipped once. If it falls heads, the game continues by throwing die A alone. If it falls tails, die B is to be used. (a) Show that the probability of red at any throw is 1 / 2. (b) If the first throw resulted in red, what is the probability of red in the third throw? (c) If red turns up in the first n throws, what is the probability that die A is being used? 2. [Conditional Probability and Poisson Random Variables] Each customer who enters Laura’s clothing store will purchase a suit with probability p . If the number of customers entering the store is Poisson distributed with mean λ , what is the probability that Laura does not sell any suits? What is the probability of her selling k suits? 3. [Law of total probability] Alice and Bob play the following game. First, Alice rolls a fair die and then Bob rolls the fair die. If Bob rolls a number at least as large as Alice’s number, he wins the game. But if Bob rolled a number smaller than Alice’s number, then Alice rolls the
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