ELEC 471, Spring 1999
Prof. Rich Kozick

## Homework 8

Date Assigned: Thursday, April 1, 1999
Date Due: Thursday, April 8, 1999

1. Reading: Please continue studying Chapter 3, and review the digital communication system that we considered on Homework 4 (item 3). Please read Chapter 4, sections 1, 2, and 3.

2. Please solve the following problems in the text.
Section 2.8: 1, 5 (show the computations for part a), 7, 9 (hint: find Var[X] and use problem 2.8.7), and graduate students do 10

Section 3.1: 1 and 4

Section 3.2: 1

Section 3.3: 1 (should be straightforward from reading the text)

3. Earlier in the semester, we learned how to generate single discrete random variables with a particular PMF using MATLAB. For example, recall how we generated the noise in Homework 4 (item 3).

How would you generate a pair of random variables (X, Y) with a given joint PMF PX,Y(x, y)? Write a MATLAB program to generate pairs of random variables (X, Y) with the PMF given in Problem 3.1.1. Test your program by generating 10,000 random variable pairs and computing the probability that Y > X. Compare your simulation result with the analytical result in Problem 3.1.1(c).

Hint: The range of the pair of random variables is

SX,Y = { (1, 1), (1, 3), (2, 1), (2, 3), (4, 1), (4, 3) }.
What is the probability of each pair in SX,Y? How can you generate the pairs with the indicated probabilities?

Presentations: The following students are asked to present their solution to this problem. The presentation will be done as a group.

Morning: Nobody!
Afternoon: Sean Michael and Erik Neff

Thank you.