MTL 601 (Probability and Statistics)
4 Credits (310)
Lectures: Tue, Thu and Fri 11.00  11.50 AM at MZ 194.
INFORMATION SHEET
Axiomatic
definition of a probability measure, examples, properties of the probability
measure, finite probability space, conditional probability and Baye's formula, countable probability space, general
probability space
Random
variables, examples, sigmafield generated by a random variable, tail
sigmafield, probability space on R induced by a random variable
Distribution
 definition and examples, properties, characterization, Jordan decomposition
theorem, discrete, continuous and mixed random variables, standard discrete and
continuous distributions
Two
dimension random variables, joint distributions, marginal
distributions, operations on random variables and
their corresponding distributions, multidimensional random variables and their
distributions
Expectation
of a random variable, expectation of a discrete and a continuous random
variable, moments
and moment generating function, correlation, covariance and regression
Various
modes of convergence, convergence in distribution, weak convergence of
generalized distributions, HellyBray theorems, Scheffe's theorem
Characteristic
function – definition and examples, properties, conjugate distributions,
uniqueness and inversion theorems, moments using characteristic function, Paul
Levy's continuity property of characteristic functions
Independent
events, sigmafields and random variables, characterization of independent
random variables, Borel 01 criteria, Kolmogorov 01
criteria
Weak
law of large numbers, strong law of large numbers, central limit theorem – Liapunov's and Lindberg's condition, LindebergLevy
form
Sampling
distributions, characteristics, asymptotic properties
Theory
of estimation – Classification of estimates, methods of estimates, confidence
regions, MVUE, Cramer Rao Theorem, Rao Blackwellization
Tests
of significance – General theory of testing hypothesis,
choice of a test, simple and composite hypothesis, tests of simple and
composite hypothesis
Goodness
of fit test, Chisquare test, Kolmogorov Smirnov test, analysis of variance
Main Text Books
1. An
Introduction to Probability and Statistics, Vijay K. Rohatgi and A.K. Md. Ehsanes Saleh, John Wiley,
second edition, 2001.
2.
Introductory
Probability and Statistical Applications, Paul L. Mayer, AddisonWesley, Second
Edition, 1970.
3.
Statistical Inference, George Casella and
Roger L. Beger Saleh, Duxbury Press, second edition, 2001.
Note: It seems, some students found that the answers provided for few problems in the following tutorial sheets are not correct. Please let me know these errors by email.
Tutorial Sheet 1 Answer
Scheme of Evaluation
Two Minor Tests of 25 Marks each 
2 X 25 
50 
One Major Examination 
1 X 50 
50 

Total 
100 
IMPORTANT INFORMATION
·
Students are encouraged to contact the Course
Coordinator or Tutorial Teachers
for any difficulties regarding the course.
·
Only those students who could not appear for
one of the minor tests due to medical
reasons are eligible for the make up
examination which will be conducted
before the major examination. However, submission of a valid medical certificate adhering to the
institute norms is mandatory.
·
The evaluated minor answer
books will be returned to the students and they must retain with them as a proof of the marks secured.
INFORMATION about the Instructors
Name 
Room No. 
Phone No. 
Email 
S Dharmaraja 
MZ 164 
7104 
dharmar@maths.iitd.ac.in 