Indian Institute of Technology Bombay
Department of Electrical Engineering
Handout 10
Measurability and Random Variables
1
EE 325 Probability and Random Processes
Aug 12,2013
Measurable Spaces
Recall
Indian Institute of Technology Bombay
Department of Electrical Engineering
Handout 5
Lecture Notes 3
1
EE 325 Probability and Random Processes
July 28, 2014
Axiomatic Probability
We have learned some
Indian Institute of Technology Bombay
Department of Electrical Engineering
Handout 4
Lecture Notes 2
1
EE 325 Probability and Random Processes
July 24, 2014
Classical Probability
The word classical in
Indian Institute of Technology Bombay
Department of Electrical Engineering
Handout 8
Lecture Notes 5
1
EE 325 Probability and Random Processes
August 7, 2014
Constructing Probability Spaces
We will us
Indian Institute of Technology Bombay
Department of Electrical Engineering
Handout 14
Lecture Notes 9
1
EE 325 Probability and Random Processes
August 28, 2014
Variance of a Random Variable
The expect
Indian Institute of Technology Bombay
Department of Electrical Engineering
Handout 25
Lecture Notes 20
1
EE 325 Probability and Random Processes
November 5, 2014
Markovs Inequality
Recall the Markovs
Indian Institute of Technology Bombay
Dept of Electrical Engineering
Quiz I
20 marks
EE 325 Probability and Random Processes
Sep 1,2014
Question 1) Consider a random variable X with distribution Q(x),
Indian Institute of Technology Bombay
Dept of Electrical Engineering
Quiz III
15 marks
EE 325 Probability and Random Processes
Nov 8, 2014
Question 1) Let us define the differential entropy of a conti
Indian Institute of Technology Bombay
Department of Electrical Engineering
Handout 20
Lecture Notes 13
1
EE 325 Probability and Random Processes
September 22, 2014
Markov Chains
Till now, we have been
Indian Institute of Technology Bombay
Dept of Electrical Engineering
Quiz III
Tutorial Solutions
EE 325 Probability and Random Processes
Nov 19, 2014
Question 1) (Rohatgi2001) Consider a bicyclist who
Notes for ECE 534
An Exploration of Random Processes for Engineers
Bruce Hajek
January 1, 2014
c 2014 by Bruce Hajek
All rights reserved. Permission is hereby given to freely print and circulate copie
EE325 Tutorial V
Notation:
N (t) is the white Gaussian noise process.
W (t) is the Weiner process.
(t) is the Poisson process.
1. Let Y (t) and Z(t) be two independent WSS processes. Let X(t) = Y (
EE325 Tutorial I
1. Let F1 , F2 , . . . be the -algebras. Verify whether the following following
sets are -algebras:
1. F = n Fn
2. F = n Fn
3. F = F1 F2 , where F1 F2 = cfw_A B : A F1 and B F2 .
2. C
Indian Institute of Technology Bombay
Department of Electrical Engineering
Handout 24
Conditional Density and Expectation
1
EE 325 Probability and Random Processes
Oct 31,2013
Detection Theory
The con
Indian Institute of Technology Bombay
Department of Electrical Engineering
Handout 19
Markov Chains
1
EE 325 Probability and Random Processes
Oct 7,2013
Markov Chains
Till now, we have been dealing mo
Indian Institute of Technology Bombay
Department of Electrical Engineering
Handout 9
Borel Sets
1
EE 325 Probability and Random Processes
Aug 5,2013
Uniform on the Square
Let us consider the real inte
Indian Institute of Technology Bombay
Department of Electrical Engineering
Handout 3
Lecture Notes 1
1
EE 325 Probability and Random Processes
July 18, 2013
Introduction
Some basics of probability the
Indian Institute of Technology Bombay
Department of Electrical Engineering
Handout 6
Axiomatic Probability
1
EE 325 Probability and Random Processes
July 29,2013
Axiomatic Probability
We have learned
Indian Institute of Technology Bombay
Department of Electrical Engineering
Handout 4
Class 2
1
EE 325 Probability and Random Processes
July 22, 2013
Classical Probability
The word classical in the tit
Indian Institute of Technology Bombay
Department of Electrical Engineering
Handout 11
Independence of Events
1
EE 325 Probability and Random Processes
Aug 19,2013
Independent Events
We have learned ab
Indian Institute of Technology Bombay
Department of Electrical Engineering
Handout 7
Probability Space Construction
1
EE 325 Probability and Random Processes
Aug 1, 2013
Constructing Probability Space
Indian Institute of Technology Bombay
Department of Electrical Engineering
Handout 15
Independence of Random Variables
1
EE 325 Probability and Random Processes
Sep 2,2013
Functions of Two Random Vari
Indian Institute of Technology Bombay
Department of Electrical Engineering
Handout 13
Discrete Random Variables
1
EE 325 Probability and Random Processes
Aug 26,2013
Discrete Random Variables
We now l
Indian Institute of Technology Bombay
Department of Electrical Engineering
Handout 17
Generating Functions
1
EE 325 Probability and Random Processes
Sep 19,2013
Sum of Two Random Variables
We now cons
Indian Institute of Technology Bombay
Department of Electrical Engineering
Handout 21
Continuous-valued Random Variables
1
EE 325 Probability and Random Processes
Oct 28,2013
Continuous Valued Random
Indian Institute of Technology Bombay
Department of Electrical Engineering
Handout 22
Gaussian Vectors, Characteristic Functions
1
EE 325 Probability and Random Processes
Oct 28,2013
Covariance Matric
Indian Institute of Technology Bombay
Department of Electrical Engineering
Handout 23
Conditional Density and Expectation
1
EE 325 Probability and Random Processes
Oct 31,2013
Markovs Inequality
Recal
EE325 Tutorial III
1. Let Xn X w.p. 1 and Xn Y w.p. 1. Then show that X = Y w.p. 1.
2. Let Xn X weakly and Xn Y weakly. Then show that X = Y w.p. 1.
3. Let cfw_Xn n1 be monotone increasing sequence of