Indian Institute of Technology Bombay
Department of Electrical Engineering
Handout 12
Lecture Notes 8
1
EE 325 Probability and Random Processes
August 25, 2014
Discrete Random Variables
We now learn an important special case of random-variables, the ones

EE325 Tutorial II
1. Let X and Y be two random variables with densities fX () and fY ()
respectively. Define Z = X + Y and show that its density fZ () is a convolution
of fX () and fY ().
2
2. Let X be a random variable with the expectation X and variance

EE325 Tutorial VI
1. Consider i.i.d. sequence of random variables X1 , X2 , . . . such that X1
U [0, 1]. Define Yn = mincfw_X1 , . . . , Xn and
Zn =
n
X
Yk / log(n).
k=1
Find E[Zn ] and also show that var(Zn ) c/n2 for some constant c. Now, show
that Vn

Indian Institute of Technology Bombay
Department of Electrical Engineering
Handout 18
Tutorial 4
EE 325 Probability and Random Processes
September 25, 2014
Question 1) (From One Thousand Exercises in Probability:) A coin shows HEAD with
probability p. Let

Indian Institute of Technology Bombay
Department of Electrical Engineering
Handout 11
Tutorial 2
EE 325 Probability and Random Processes
August 21, 2014
Question 1) Let us find the probability that two randomly picked points on a line segment
partition it

Indian Institute of Technology Bombay
Department of Electrical Engineering
Handout 21
Tutorial 5
EE 325 Probability and Random Processes
October 9, 2014
An excellent source of questions on Markov Chains is P. Bremaud, Markov
Chains, Springer 2001.
Questio

Indian Institute of Technology Bombay
Department of Electrical Engineering
Handout 6
Tutorial I
EE 325 Probability and Random Processes
July 31, 2014
Question 1) (Rohatgi2001) Consider a bicyclist who leaves a point P (see Figure), choosing one of the roa

Indian Institute of Technology Bombay
Dept of Electrical Engineering
Quiz III
30 marks
EE 325 Probability and Random Processes
September 12, 2014
I have given references where some solutions can be found.
The notations and definitions given in a question

Indian Institute of Technology Bombay
Department of Electrical Engineering
Handout 7
Lecture Notes 4
1
EE 325 Probability and Random Processes
August 4, 2014
Properties of Probability
Based on the three probability axioms, we can derive many properties of

Indian Institute of Technology Bombay
Department of Electrical Engineering
Handout 3
Lecture Notes 1
1
EE 325 Probability and Random Processes
July 21, 2014
Introduction
Some basics of probability theory are typically taught in senior high-school, and man

EE325 Tutorial III
1. Let X1 , X2 , . . . , be i.i.d. (independent and identically distributed) random
variables,
Pn where X1 is an exponential random variable with mean 1/. Let
Sn = k=1 Xk .
Show that for s > 0,
fSn (s) =
(s)n1 s
e
.
(n 1)!
Do the requ