Syllabus

The topics to be covered are as follows:

1. Probability Spaces and Random Variables
   • Probability space, conditional probability, Bayes' theorem
   • Random variable, cumulative distribution function and its properties, probability density function
   • Functions of a random variable, standard discrete and continuous distributions and their applications
   • Transformations, moments, Chebyshev's inequality
2. Joint Distributions
   • Random vectors, joint, marginal, and conditional distributions
   • Conditional expectation, independence, correlation and regression
   • Bivariate normal distribution, functions of random vectors, transformations
3. Limit Theorems
   • Convergence of sequences of random variables
   • Weak and strong laws of large numbers, central limit theorem
4. Estimation and Tests of Hypotheses
   • Sampling distributions, point estimation of parameters
   • Maximum likelihood method and method of moments
   • Interval estimation, testing of hypotheses

Textbooks

• Rohatgi, Vijay K.; Saleh, A. K. Md. Ehsanes. An Introduction to Probability and Statistics. Second edition. Wiley India, New Delhi, 2001. [IITJ Library]
• Casella, George; Berger, Roger L. Statistical Inference. Second edition. Cengage Learning India Pvt. Ltd., New Delhi, 2002. [IITJ Library]

Reference Books

• Hogg, Robert V.; McKean, Joseph W.; Craig, Allen T. Introduction to Mathematical Statistics. Sixth edition. Dorling Kindersley India Pvt. Ltd., New Delhi, 2005. [IITJ Library]
• Prakasa Rao, B. L. S. A First Course in Probability and Statistics. World Scientific, New Jersey, 2009.
• Castañeda, Liliana Blanco; Arunachalam, Viswanathan; Dharmaraja, Selvamuthu. Introduction to Probability and Stochastic Processes with Applications. Wiley, Hoboken, NJ, 2012. [IITJ Library]

Online Course Material

• Kumar, Somesh. Probability and Statistics. NPTEL Course Material, Department of Mathematics, IIT Kharagpur, 2026. [NPTEL]

Evaluation

To be announced.