PS12 - University of Illinois Fall 2009 ECE 313: Problem...

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University of Illinois Fall 2009 ECE 313: Problem Set 12 Joint Distributions of Random Variables Due: Wednesday November 18 at 4 p.m. Reading: Ross, Chapter 6, Sections 1-4; Powerpoint Lecture Slides, Sets 30-34 Noncredit Exercises: Chapter 6: Problems 1-3, 9, 10, 13, 15, 19-23, 40-42; Theoretical Exercises 4, 6; Self-Test Problems 3, 5, 6, 7 Reminder: Hour Exam II on Monday November 16, 7:00 p.m. – 8:00 p.m., 100 MSEB Coverage of material is Problem Sets 6-11 1. [Joint pmfs] The joint pmf p X , Y ( u,v ) of X and Y is shown in the table below. u v 0 1 3 5 4 0 1/12 1/6 1/12 3 1/6 1/12 0 1/12 -1 1/12 1/6 1/12 0 (a) Find the marginal pmfs p X ( u ) and p Y ( v ). (b) Are X and Y independent random variables? (c) Find P { X Y } and P { X + Y 4 } . (d) Find p X | Y ( u | 3), E [ X | Y = 3] and var ( X | Y = 3). 2. [Drill problem on jointly continuous random variables I] Ross, Problem 6.8, page 287 (Problem 8 on page 313 of the 7th edition) The joint pdf of X and Y is given by f ( u,v
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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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PS12 - University of Illinois Fall 2009 ECE 313: Problem...

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