MTL 5005 (Introduction to Probability)

4 Credits (3-1-0)

I Semester 2025 - 2026

Lectures: Tuesday and Friday between 3:30 PM and 4:45 PM in LH 510.

Course Contents

Random experiments and events, axiomatic definition of probability, properties of probability functions, conditional probability, Bayes’ theorem, discrete and continuous random variables, distribution functions, probability mass and density functions, expectations and moments, moment-generating functions, moment inequalities, standard probability distributions, joint, marginal, and conditional distributions, independence, covariance and correlation, conditional expectation, law of large numbers, and central limit theorem.

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.    Introduction to Probability and Stochastic Processes with Applications, Liliana Blanco Castaneda, Viswanathan Arunachalam, Selvamuthu Dharmaraja, Wiley, Asian Edition, Jan. 2016.

3.    Introduction to Probability, Statistical Methods, Design of Experiments and Statistical Quality Control, Selvamuthu Dharmaraja, Dipayan Das, Springer, 2018.

Reference Text Books

1.    Modern Probability Theory, B.R. Bhat, New Age Publishers, third edition, 1981.

2.    An Introduction to Probability Theory and its Applications, Vol. I & II, William Feller, John Wiley, second edition, 2000.

Lecture Notes

Sl. No. Topics Videos

1 Axioms of probability, Probability space, Conditional probability, Independence, Baye's rule Part 1, Part 2, Part 3, Part 4, Part 5

2 Random variable, Distribution of Functions of Random Variable, Moments, Generating functions Part 1, Part 2, Part 3, Part 4, Part 5, Part 1, Part 2, Part 3, Part 4, Part 5

3 Some common discrete and continuous distributions Part 6, Part 7, Part 8, Part 9, Part 10, Part 11

4 Two and higher dimensional distributions, Functions of random variables, Order statistics, Conditional distributions, Covariance, correlation coefficient, conditional expectation Part 1, Part 2, Part 3, Part 4, Part 5, Part 1, Part 2, Part 3, Part 4, Part 5, Part 6, Part 7, Part 8, Part 9, Part 10, Part 11, Part 12, Part 13, Part 14

5 Modes of convergences, Law of large numbers, Central limit theorem Part 1, Part 2, Part 3, Part 4, Part 5

Note: The above classification of lecture notes are tentative only. (courtesy: NPTEL course)

Sl. No.	Topics	Videos
1	Axioms of probability, Probability space, Conditional probability, Independence, Baye's rule	Part 1, Part 2, Part 3, Part 4, Part 5
2	Random variable, Distribution of Functions of Random Variable, Moments, Generating functions	Part 1, Part 2, Part 3, Part 4, Part 5, Part 1, Part 2, Part 3, Part 4, Part 5
3	Some common discrete and continuous distributions	Part 6, Part 7, Part 8, Part 9, Part 10, Part 11
4	Two and higher dimensional distributions, Functions of random variables, Order statistics, Conditional distributions, Covariance, correlation coefficient, conditional expectation	Part 1, Part 2, Part 3, Part 4, Part 5, Part 1, Part 2, Part 3, Part 4, Part 5, Part 6, Part 7, Part 8, Part 9, Part 10, Part 11, Part 12, Part 13, Part 14
5	Modes of convergences, Law of large numbers, Central limit theorem	Part 1, Part 2, Part 3, Part 4, Part 5