ECE 534: Random Processes Quiz, University of Illinois at Urbana-Champaign, Fall 2007 - Pr, Quizzes of Electrical and Electronics Engineering

Download ECE 534: Random Processes Quiz, University of Illinois at Urbana-Champaign, Fall 2007 - Pr and more Quizzes Electrical and Electronics Engineering in PDF only on Docsity! University of Illinois at Urbana-Champaign ECE 534: RANDOM PROCESSES Fall 2007 Probability Quiz Monday, September 10, 2007 Name: • This is a closed-book exam. No notes of any kind are allowed. • Calculators, laptop computers, Palm Pilots, two-way email pagers, etc. may not be used. • Write your answers in the space provided. If you need extra space, use the back of the previous page. • Please show all of your work. Answers without appropriate justification will receive very little credit. Score: 1: (12 points) 2: (12 points) 3: (12 points) Total: (36 points) 1 1 Suppose continuous RVs X and Y have the joint pdf fX,Y (x, y) = { x C if 1 ≤ x ≤ 3 and 0 ≤ y ≤ 2 0 otherwise Let R be defined by R = Y/X and let D be the event R ≤ 1/3. a) Determine the value of C. b) Are X and Y independent? Are they independent conditioned on D? 2 Extra space if necessary. Please denote which problem you are using this extra space for. 5 Extra space if necessary. Please denote which problem you are using this extra space for. 6