EC 221 Probability and Random Processes Assignment-I
1. Given S cfw_1, 2,3 findtwofieldscontainingthesubsetcfw_2.
2. Suppose isafieldofsubsetsofasetSand B .Showthat C cfw_ A B | A isa
fieldofthesubse
Probability Review
Definition: Let S be a sample space and a sigma field defined over it. Let P : be a mapping from the sigma-algebra into the real
line such that for each A , there exists a unique P(
Computational
Complexity
Gaurav Trivedi
EEE Dept.
IIT Guwahati
Well talk about this first
one today.
http:/www.claymath.org/millennium/
In order to celebrate mathematics in the new millennium, The Cla
ESTIMATION THEORY
4.1. Introduction:
When we fit the random data by an AR model, we have to determine the process
parameters observed data.
In RADAR signal processing, we have to determine the locatio
EE664: Introduction to Parallel
Computing
Dr. Gaurav Trivedi
Lectures 5-14
1
Some Important Points
Automatic vs. Manual Parallelization
Understand the Problem and the Program
Partitioning
Communicatio
Evolution
Entrepreneurial Stage :
Characteristics :
1) The focus of Idea Device Technology was on creativity. The team worked with the
objective of a new dev-ops solution for prospective clients. The
Effective Public Speaking
Adarsh Saurav
Ashish Kumar
FOCAL, IIM Bangalore
What is public
speaking?
The art of effective oral
communication with an
audience.
It is also called oratory or
oration.
Three
Effective Public Speaking
Adarsh Saurav
Ashish Kumar
FOCAL, IIM Bangalore
What is public
speaking?
The art of effective oral
communication with an
audience.
It is also called oratory or
oration.
Three
Decision Sciences I: ASSIGNMENT - I
Sections D, E & F
This assignment, in its entirety, is due to be submitted on or
before 11 pm on July 27, 2017. However it is very strongly
recommended, that the wo
Department of Electronics and Communication Engineering
Indian Institute of Technology Guwahati
EC-331 Communication Laboratory
Experiment-2: AM generation and demodulation
Objectives:
1. To generate
Department of Electronics and Communication Engineering
Indian Institute of Technology Guwahati
EC-331 Communication Laboratory
Experiment-6: Demodulation of PWM Signals
Prepared by: Mr. Utpal Sarma,
Department of Electronics and Communication Engineering
Indian Institute of Technology Guwahati
EC-331 Communication Laboratory
Experiment-5: Generation of PWM & PPM Signals
Prepared by: Mr. Utpal Sar
Department of Electronics and Communication Engineering
Indian Institute of Technology Guwahati
EC-331 Communication Laboratory
Experiment-1
General Instructions:
1. Come prepared to the lab. It is a
Maximum Likelihood Estimator (MLE)
Suppose X 1, X 2 ,., X n are random samples with
function f X , X
1
2 ,., X n /
( x1 , x2 ,., xn )
the joint probability density
which depends on an unknown nonrando
Pattern Recognition and Machine Learning :
Assignment 1
The assignment is due on February 12.
The assignments are meant to enhance your learning, so that you master the basics
by the close of this s
Assignment Problems are given below.
S. No.
Problem Statement
1
Basic Programs on Matrix into Vector Computations using Pthreads, OpenMP and
MPI
2
Matrix-Matrix multiplication simple, Cannons, DNS alg
Tutorial9Date16/3/11
1. Suppose X and Y denote the independent random variables with the identical density
function f. Find the expressions for the PDF of (i) Z = min( X , Y ) and (ii)
Z = max( X , Y
Tutorial 11 30/3/11
1. The Poisson process
cfw_ X (t ), t 0 is
a random
process where
the increments
X (t j ) X (ti ), t j > ti are independent Poisson random variables with the rate parameter
(t2 t1
Tutorial 4
1. A player has equal probability of win in each game against his opponent. Which is more
porobable?
(a) Three wins from 5 games or 4 wins from 7 games?
(b) At least three wins from from 5
EC 221:Probability and Random Processes
Assignment-2
1. Consider the sequence cfw_ An given by
An ( a
1
n 1
, b n1 ), a, b
Show that lim supcfw_ An lim infcfw_ An ( a, b] and hence lim An exists.
Tutorial 8
1.
9/3/11
(a) ForrandomvariablesXandY,thejointPDFisgivenby
1
, x 1, y 1
f X ,Y ( x, y ) 4
0 otherwise
Show that XandYareindependentrandomvariables.
(b) Suppose XandYaredistributedas
1
2
2
! " #$%
"#$
#
D( f | g ) =
&!
f ( x)log ( f ( x) / g ( x)dx
'!
+
,- !
( '!
(.
I A ( s) =
( /
&! * (
.
1 ( (
.
.
1 if s A
0 otherwise
&
2
,
2+
*
( /
&
X
/
( a>03
P(cfw_ X + a)
4
&
I A B = I A I B = mi
EC 221:Probability and Random Processes
Assignment-3
1. A well shuffled deck of 52 cards is distributed among 4 players North, East, South and
West. What are the probabilities that
(a) North has 2 kin
Tutorial 5
1. Suppose X is a binomial random variable with the PMF
()
p X ( k ) = n p k (1 p ) n k
k
0 p 1, k = 0,1,., n
(a) Find the most likely value(s) of X.
(b) Find a condition on n and p so that
Tutorial 6
1. (a) Suppose X is a discrete random variable with RX = cfw_0,1,. show that
EX = P (cfw_ X n)
n =0
(b) Suppose X is a non-negative continuous random variable. Show that
EX = (1 FX ( x) dx
MA 201 Complex Analysis
Lecture 16: Residues Theorem
Lecture 16
Residues theorem and its Applications
Residues
Question: Let is a simple closed contour in a simply connected domain D
and let z0 doesnt
MA 201 Complex Analysis
Lecture 17: Evaluation of integrals
Lecture 17
Evaluation of integrals
Evaluation of certain contour integrals: Type I
Type I: Integrals of the form
Z
2
F (cos , sin ) d
0
dz
.
MA 201 Complex Analysis
Lecture 18: Evaluation of integrals
Lecture 18
Evaluation of integrals
Evaluation of certain contour integrals: Type IV
Type IV Integrals of the form
Z
0
sin x
dx
x
can be eval