ECE 302 Spring 2012
Practice problems: quantization, source coding, and limit theorems.
Ilya Pollak
These problems have been constructed over many years, using many dierent sources.
If you nd that some problem or solution is incorrectly attributed, please
ECE 301, Homework #1, due date: 8/29/2012
https:/engineering.purdue.edu/chihw/12ECE301F/12ECE301F.html
Review of calculus and arithmetics:
Question 1: Compute the values of the following integrals. You can leave your answers
in the form of trigonometric f
poisscdf
Poisson cumulative distribution function
Syntax
P = poisscdf(X,lambda)
Description
P = poisscdf(X,lambda) computes the Poisson cdf at each of the values in X using the corresponding mean parameters in lambda . X and lambda can be vectors, matrice
Probabilistic Methods In Electrical And Computer Engineering
ECE 302

Spring 2009
ECE 302, Homework #5, Due 2/18 http:/www.ece.purdue.edu/chihw/ECE302 09S.html
Question 1: [Basic] Write down the sample space and weight assignment (pmf) for a binomial random variable X with parameters n = 4, p = 1/4. Plot the pmf of X. Compute its
Probabilistic Methods In Electrical And Computer Engineering
ECE 302

Fall 2006
Probability for Engineering Applications
Assignment #2, due at the beginning of class on Thursday, February 2nd, 2006
1. (1 pt) (Textbook exercise 2.19) Show that the probability that exactly one of the events A or B occurs is given by P [A] + P [B]  2P
Probabilistic Methods In Electrical And Computer Engineering
ECE 302

Fall 2010
ECE 302: Homework 2
Prof. Saul Gelfand Spring 2010
Due February 5, 2010
Problem 1 a. The error process described is Bernoulli. Let K be the number of errors out of n operations. We have then P [K = k ] = for k = 1, . . . , n. b. We have that type 1 errors
Probabilistic Methods In Electrical And Computer Engineering
ECE 302

Spring 2010
EE302 Homework #4
Assigned 10/14/09, Due 10/23/09 (by 4:30 in dropbox in MSEE 330) 1. Text, problem 3.41, page 134. 2. Text, problem 4.32, page 218 3. A Gaussian random volatage X volts is input to a half wave recti er and the output voltage is Y = Xu (X
Probabilistic Methods In Electrical And Computer Engineering
ECE 302

Spring 2011
ECE 302, Homework #1, due date: 1/19/2011 http:/cobweb.ecn.purdue.edu/chihw/11ECE302S/11ECE302S.html
Review of Calculus: Question 1: Compute the values of the following integrals, given the condition that > 0.
1
1 dx x2 ex dx
0
Question 2: Compute the e
EE302 Homework #4
Assigned 10/13/11, Due 10/19/11 (by 4:30 in dropbox in MSEE 330)
1. A Gaussian random volatage X volts is input to a half wave recti er and the output voltage
is Y = Xu (X ) Volts were u (x) is the unit step function. Assume X has mean 0
Probabilistic Methods In Electrical And Computer Engineering
ECE 302

Spring 2010
ECE 302: Homework 6
Prof. Saul Gelfand Fall 2009
Due November 20, 2009
Problem 1: Text 5.95 Since X and Y are independent, we have that the joint pdf fXY (x, y ) = fX (x)fY (y ) = 1 for (x, y ) inside the box indicated below:
1.5
1 y 0.5 0 0
0.5 x
1
1.5
W
Probabilistic Methods In Electrical And Computer Engineering
ECE 302

Fall 2006
Probability for Engineering Applications
Assignment #4, due at the beginning of class on Thursday, February 16th, 2006
1. (1 pt) (Textbook exercise 2.64) Let A and B be two events with probabilities P [A] and P [B]. a. Find P [A B] if A and B are independ
Probabilistic Methods in Electrical and Computer Engineering
ECE 302

Spring 2012
ECE 302 Spring 2012
Practice problems: Continuous random variables; uniform, exponential, normal, lognormal,
Rayleigh, Cauchy, Pareto, Gaussian mixture, Erlang, and Laplace random variables;
quantization; optimal portfolios; simulating a fair coin with a
Probabilistic Methods in Electrical and Computer Engineering
ECE 302

Spring 2012
ECE 302 Spring 2012
Practice problems: Continuous random variables; uniform, exponential, normal, lognormal,
Rayleigh, Cauchy, Pareto, Gaussian mixture, Erlang, and Laplace random variables;
quantization; optimal portfolios; simulating a fair coin with a
Probability and Statistics in Electrical Engineering
ECE 302

Fall 2012
2. Discrete Random Variables
Part I
ECE 302 Spring 2012
Purdue University, School of ECE
Prof. Ilya Pollak
Random Variables: DeniHon
A random variable is an assignment of a value
(number) to every outcome in t
Probability and Statistics in Electrical Engineering
ECE 302

Fall 2012
ECE 302 Spring 2012 Review for
Exam 2
Ilya Pollak
Purdue University
PermutaAons
PermutaAons: number of ways of ordering n
objects = n (n
1) (n
2) 2 1 = n! (called
n factorial).
k
permutaAons
Probability and Statistics in Electrical Engineering
ECE 302

Fall 2013
ECE302 Probabilistic Methods in Electrical Engineering
Fall 2013
Mark R. Bell
MSEE 336
Homework Assignment #6
Due Thursday, October 31, 2013
Reading Assignment: Continue reading in LeonGarcia: Review Chapter 3 material and read
sections 4.1 through 4.6.
Probability and Statistics in Electrical Engineering
ECE 302

Fall 2012
2. Discrete Random Variables
Part VI: Independence
ECE 302 Spring 2012
Purdue University, School of ECE
Prof. Ilya Pollak
Independence of a random variable
and an event
Random variable X is independent of event A if
P(
Probability and Statistics in Electrical Engineering
ECE 302

Fall 2012
2. Discrete Random Variables
Part V: Condi7onal Expecta7on
ECE 302 Spring 2012
Purdue University, School of ECE
Prof. Ilya Pollak
Condi7onal expecta7on of a random
variable, given an event A
E [ X  A] = xpX  A
Probability and Statistics in Electrical Engineering
ECE 302

Fall 2012
2. Discrete Random Variables
Part IV: Joint PMFs
ECE 302 Spring 2012
Purdue University, School of ECE
Prof. Ilya Pollak
Joint PMF pX,Y of X and Y
If X and Y are discrete random variables, their
joint prob
Probability and Statistics in Electrical Engineering
ECE 302

Fall 2012
ECE 302
Probabilis/c Methods in Electrical and
Computer Engineering
Purdue University
School of Electrical and Computer Engineering
Spring 2012
Prof. Ilya Pollak
How to approach this course
Learning is both more eec
Probability and Statistics in Electrical Engineering
ECE 302

Fall 2012
ECE 302
Probabilis/c Methods in Electrical and
Computer Engineering
Purdue University
School of Electrical and Computer Engineering
Spring 2012
Prof. Ilya Pollak
Probability and Sta/s/cs
Tools to extract paFerns from
Probability and Statistics in Electrical Engineering
ECE 302

Fall 2012
2. Discrete Random Variables
Part II: Expecta:on
ECE 302 Spring 2012
Purdue University, School of ECE
Prof. Ilya Pollak
Expected value of X: Deni:on
Ilya Pollak
Expected value of X: Deni:on
E [ X ] is also called th
Probabilistic Methods In Electrical And Computer Engineering
ECE 302

Fall 2014
ECE 302 QUIZ 1
6/16/17
Instructor: Kyle Ziga
10 points
Name: SO. (mix/3Q A
l.Write down the axioms of probability.
HA5? 0
PM: 1
WW6) , m was :l w :a
Ovao/LJ3P(Q 4i :iA (i: 65$ AW/i a
(.4 i?! ! &U?/J
2.ln an experiment you roll a sixsided die and flip
a co
Probabilistic Methods In Electrical And Computer Engineering
ECE 302

Fall 2014
ECE 302
Summer 2017
Instructor: Kyle Ziga
Homework 3
Due: June 30, 2017
Topics: Probability mass functions, expectation, variance, standard
deviation
1. An experiment takes place in which a coin is flipped until a
Heads comes up. Let X be the number of fa