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Unformatted text preview: University of Illinois Fall 2009 ECE 313: Problem Set 3 Discrete Random Variables: pmf, expectation, LOTUS, and variance Due: Wednesday September 16 at 4 p.m.. Reading: Ross, Chapter 4 Noncredit Exercises: DO NOT turn these in. Chapter 4: Problems 2, 7, 13, 28, 35, 39, 4043 Theoretical Exercises 11, 13, 15; SelfTest Problems 110. 1. [Rolling a die till something different happens] Consider the dierolling experiment described in Problem 3 of Problem Set 2 in which a die is rolled repeatedly until an outcome different from the outcome of the first roll is observed. (a) Let X denote the number of rolls of the die on a trial. What values can X take on? What is the probability mass function (pmf) of X ? What is the probability that X is an even number? (b) A random variable Y is defined on this experiment as follows: Y = ( i, if outcome of the fourth roll is i, , if experiment ended in two or three rolls. What is the pmf of Y ? Hint: Find p Y (0) first and then argue that p Y ( i ) = (1 p Y (0)) / 6 , 1 i 6. 2. [The Game of ChuckALuck] In the game of ChuckALuck played at fairs and carnivals in the MidWest, bets are placed on numbers 1, 2, 3, 4, 5, 6, and then three fair dice are rolled. If the number chosen does not show up on any of the three dice, the bettor loses his stake. Otherwise, the dealer pays the bettor one or two or three times the amount staked according as the number chosen shows up on one or two or all three of the...
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This note was uploaded on 11/08/2010 for the course ECE ECE 313 taught by Professor S during the Spring '10 term at University of Illinois at Urbana–Champaign.
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