ELEC 471, Spring 2002
Prof. Rich Kozick

## Homework 9

Date Assigned: Tuesday, April 9, 2002
Date Due: Tuesday, April 16, 2002

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

2. Please solve the following problems in the text.

Section 3.1: 1 and 4

Section 3.2: 1

Section 3.3: 1 and 5

Section 3.4: 1

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 4).

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?

4. Presentations: The following students will present their solution to the Matlab problem in item 3 on April 16:
Rob Terrible and Justin Valls
Thank you.