This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: University of Illinois Fall 2009 ECE 313: Problem Set 9 Continuous Random Variables Due: Wednesday October 28 at 4 p.m. Reading: Ross, Chapter 5; Powerpoint Lecture Slides, Sets 2224 Noncredit Exercises: Chapter 5: Problems 13, 5, 6, 1519, 2325, 3234; Theoretical Exercises 1, 8; SelfTest Problems 14 1. [Validity of PDFs] Nine functions f ( u ) are shown below. Note that in each case, f ( u ) = 0 for all u not in the interval specified. In each case, determine whether f ( u ) is a valid probability density function (pdf). If f ( u ) is not a valid pdf, determine if there exists a constant C such that C f ( u ) is a valid pdf. (a) f ( u ) = 2 u, < u < 1. (b) f ( u ) =  u  ,  u  < 1 2 (c) f ( u ) = 1  u  ,  u  < 1 , (d) f ( u ) = ln u, < u < 1. Hint: ln u can be integrated by parts. (e) f ( u ) = ln u, < u < 2 , (f) f ( u ) = 2 3 ( u 1) , < u < 3 , (g) f ( u ) = exp( 2 u ) , u > 0. (h) f ( u ) = 4exp( 2 u ) exp( u ) , u > , (i) f ( u ) = exp( u  ) ,  u  < 1 , 2. [Calculating probabilities from pdfs] The continuous random variable X has pdf f X ( u ) = ( c (1 u ) , u 1 , , elsewhere . (a) What is the value of c ? (b) Find P { X > . 5 } . (c) Find P { 6 X 2 > 5 X 1 } . 3. [Using LOTUS] Let X be a continuous random variable that is uniformly distributed on [ 1 , +1]....
View
Full
Document
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.
 Spring '10
 S

Click to edit the document details