{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# PS12 - University of Illinois Fall 2009 ECE 313 Problem Set...

This preview shows pages 1–2. Sign up to view the full content.

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 ) = c ( v 2 - u 2 ) exp( - v ) , - v u v, 0 < v < .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online