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 som
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. Yo
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 t
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 paramet
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 para
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
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
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
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 we
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
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
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;
quantizat
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;
quantizat
Probability and Statistics in Electrical Engineering
ECE 302

Fall 2012
3. General Random Variables
Part VIII: Sums of Independent
Random Variables
ECE 302 Spring 2012
Purdue University, School of ECE
Prof. Ilya Pollak
Sum of two independ
Probability and Statistics in Electrical Engineering
ECE 302

Fall 2012
4. Quantization and Data
Compression
ECE 302 Spring 2012
Purdue University, School of ECE
Prof. Ilya Pollak
What is data compression?
Reducing the file size without compromising the
quality of the da
Probability and Statistics in Electrical Engineering
ECE 302

Fall 2012
5. Limit Theorems, Part II: Central
Limit Theorem
ECE 302 Spring 2012
Purdue University, School of ECE
Prof. Ilya Pollak
WLLN and CLT
X1, , Xn i.i.d. with nite m
Probability and Statistics in Electrical Engineering
ECE 302

Fall 2012
5. Limit Theorems, Part I: Weak Law of
Large Numbers
ECE 302 Spring 2012
Purdue University, School of ECE
Prof. Ilya Pollak
Some moJvaJon
Suppose X1, , Xn are i.
ECE 301, Homework #8, due date: 10/24/2012
https:/engineering.purdue.edu/chihw/12ECE301F/12ECE301F.html
Question 1: [Basic] For a continuous time x(t) = 2t , nd out the Fourier transformation
of x(t
Probability and Statistics in Electrical Engineering
ECE 302

Fall 2012
5. Limit Theorems, Part III: Strong Law
of Large Numbers
ECE 302 Spring 2012
Purdue University, School of ECE
Prof. Ilya Pollak
Convergence with probability 1
Experi
ECE 301, Homework #7, due date: 10/17/2012
https:/engineering.purdue.edu/chihw/12ECE301F/12ECE301F.html
Question 1: [Basic] p. 257, Problem 3.25.
Question 2: [Basic] p. 257, Problem 3.30(a,b).
Questio
ECE 301, Homework #6, due date: 10/10/2012
https:/engineering.purdue.edu/chihw/12ECE301F/12ECE301F.html
Question 1: [Basic] Consider three periodic signals x1 (t) and x2 (t). x1 (t) has period 2
and i
ECE 301, Homework #5, due date: 10/3/2012
https:/engineering.purdue.edu/chihw/12ECE301F/12ECE301F.html
Question 1: [Basic] p. 141, Problem 2.21 (b,d).
Question 2: [Basic] p. 141, Problem 2.22 (a,e).
Q
ECE 301, Homework #4, due date: 9/26/2012
https:/engineering.purdue.edu/chihw/12ECE301F/12ECE301F.html
Question 1: [Basic] p. 61, Problem 1.27 (a,b,c)
Question 2: [Basic] p. 61, Problem 1.28 (a,b,c).
ECE 301, Homework #3, due date: 9/19/2012
https:/engineering.purdue.edu/chihw/12ECE301F/12ECE301F.html
Question 1: [Advanced] Consider two functions f (t) and g (t) described as follows.
cfw_
1 if 2 t
Probabilistic Methods In Electrical And Computer Engineering
ECE 302

Fall 2014
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Probabilistic Methods In Electrical And Computer Engineering
ECE 302

Fall 2014
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Probabilistic Methods In Electrical And Computer Engineering
ECE 302

Fall 2014
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Probabilistic Methods In Electrical And Computer Engineering
ECE 302

Fall 2014
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