# hw03 - University of Illinois Spring 2010 ECE 313 Problem...

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

University of Illinois Spring 2010 ECE 313: Problem Set 3: Solutions Discrete Random Variables: pmf, expectation, LOTUS, and variance 1. [ Cumulative distribution function ] Page 174, #4.19 We have that P X = y { } = p y ( ) = F b ( ) ! F b ! ( ) F 0 ( ) ! F 0 ! ( ) = 1 2 ! 0 = 1 2 F 1 ( ) ! F 1 ! ( ) = 3 5 ! 1 2 = 1 10 F 2 ( ) ! F 2 ! ( ) = 4 5 ! 3 5 = 1 5 F 3 ( ) ! F 3 ! ( ) = 9 10 ! 4 5 = 1 10 F 3.5 ( ) ! F 3.5 ! ( ) = 1 ! 9 10 = 1 10 Therefore, p y ( ) = 1/ 2, y = 0 1/10, y = 1 1/ 5, y = 2 1/10, y = 3 1/10, y = 3.5 0, otherwise ! " # # # \$ # # # 2. [ Binomial random variable ] Page 176, #4.43 Assume that each digit is interpreted independently. Let E = {3 or more digits are received incorrectly}, and let x = # of incorrectly received bits, then E = {x 3} and x is a binomial random variable with parameters (5, 0.2). ! P E ( ) = 5 k " # \$ % k = 3 5 ( 0.2 ( ) k 0.8 ( ) 5 ) k = 5 3 ! " # \$ % 0.2 ( ) 3 0.8 ( ) 2 + 5 4 ! " # \$ % 0.2 ( ) 4 0.8 ( ) 1 + 5 5 ! " # \$ % 0.2 ( ) 5 = 10 0.2 ( ) 3 0.8 ( ) 2 + 5 0.2 ( ) 4 0.8 ( ) 1 + 0.2 ( ) 5 = 0.0579 3. [ Flying used to be fun ] Let X denote the number of passengers that do not

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.

## This note was uploaded on 04/20/2010 for the course ECE ECE 313 taught by Professor S during the Spring '10 term at University of Illinois at Urbana–Champaign.

### Page1 / 3

hw03 - University of Illinois Spring 2010 ECE 313 Problem...

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

View Full Document
Ask a homework question - tutors are online