# PS13 - University of Illinois Fall 2009 ECE 313 Problem Set...

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

Unformatted text preview: University of Illinois Fall 2009 ECE 313: Problem Set 13 Functions of Random Variables Due: Friday December 4 at 4 p.m. Reading: Ross, Chapter 6 except Sections 6.6 and 6.8; Powerpoint Lecture Slides, Sets 34-37 Noncredit Exercises: Chapter 6: Problems 26, 28-30, 51, 54 Theoretical Exercises 8, 14 ,22, 23, 33,; Self-Test Problems 3, 5, 6, 7, 12 1. [A piece of cake? or a sheet cake with a piece missing?] The jointly continuous random variables X and Y have joint pdf f X , Y ( u,v ) = 4 3 , < u < 1 , < v < 1 , max { u,v } > 1 2 , , elsewhere. (a) Sketch the u- v plane and indicate on it the region where f X , Y ( u,v ) is nonzero. (b) Find the marginal pdf f Y ( v ) of Y . (c) What is P { Y ≤ α X } where 0 < α ≤ 1? (d) What is P { Y ≤ α X } where 1 < α < ∞ ? (e) If Z = Y / X , find P { Z ≤ α } for all α, < α < ∞ . (f) Find the pdf f Z ( α ). Be sure to specify the value of f Z ( α ) for all α,- ∞ < α < ∞ . 2. [One function of two random variables] The joint pdf of X and Y is given by f X , Y ( u,v ) = ( 2 u, < u < 1 , < v < 1 , , elsewhere. Find the pdf of Z = X 2 Y . 3. [Independent exponential random variables] Let X 1 and X 2 be independent exponential random variables with parameters λ 1 and λ 2 respectively. (a) Find the pdf of Y = X 1 + X 2 by convolving the pdfs of X 1 and X 2 for the case λ 1 = λ 2 = λ ....
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

PS13 - 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