# PS04 - University of Illinois Fall 2009 ECE 313 Problem Set...

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

University of Illinois Fall 2009 ECE 313: Problem Set 4 Counting Random Variables, Maximum-Likelihood Estimation Due: Wednesday September 23 at 4 p.m. . Reading: Ross, Chapter 4 Noncredit Exercises: DO NOT turn these in. Chapter 4: Problems 32, 38-39, 40-43, 47-52; Theoretical Exercises 16-19; Self-Test Problems 9, 13, 15, 16. 1. [Graphical study of binomial pmfs] Use a spreadsheet/Mathematica/MATLAB for this problem. Let A denote an event of probability p . (a) For p = 0 . 1 , 0 . 25 , 0 . 4 , 0 . 5 , 0 . 6 , 0 . 75, and 0 . 9, ﬁnd the numerical values of the probabilities that A occurs 0 , 1 , 2 ,..., 10 times on 10 trials. (b) You have computed the pmf of a binomial random variable X p with parameters (10 ,p ) for seven choices of p . For each value of p , draw a bar graph of the pmf of X p . (The pmf of X 0 . 5 is shown on page 157 of the text!). (c) What is the relationship between the pmfs of X p and X 1 - p ? 2. [The probability of an even number of successes] Let X denote a binomial random variable with parameters ( N,p ). What is P { X is even } ? Hint: Expand ( x + y ) n + ( x - y ) n using the binomial theorem and then set x = 1 - p , y = p . 3. [The pricing of airline tickets] Eight persons have purchased tickets (\$ F per person) for travel in a 5-passenger plane on a scheduled airline ﬂight in Ruritania. The number of persons who actually show up to travel can be modeled as a binomial random variable X with parameters (8 , 0 . 5). Naturally, if more than 5 persons show up, only

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 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.

### Page1 / 2

PS04 - 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