**Course Details:**

Statistics: Review of statistics, describing data – frequency tables, graphs, and summarizing data – measures of central tendency and variation, multivariate data and correlation coefficient.

Probability: Axioms of probability, conditioning and Bayes' rule, independence, random variables, standard probability density functions - binomial, poisson, normal, etc., expected value, Chebhyshev’s inequality, moment generating function, covariance, correlation, functions of random variables, law of large numbers, central limit theorem, conditional expectation.

Statistical Inference: Point estimation – maximum likelihood estimation (mle), method of moments, Bayes’ estimator, distributions of sampling statistics, interval estimation, tests of hypotheses – tests for mean and variance, t-test, chi-square test, evaluation of point estimators – unbiasedness, mean squared error (mse), Cramer-Rao bound.

Simulation: Generating random numbers – inverse transform, and Box-Muller methods. Importance sampling and Monte Carlo simulation.

**Text Books:**

- Robert V. Hogg, Allen Craig, Joseph W. McKean, Introduction to Mathematical Statistics, Pearson
- A. Popoulis and S. Pillai, Probability, Random Variables and Stochastic Processes, McGraw Hill Education; 4 edition
- Sheldon M. Ross, Introduction to Probability and Statistics for Engineers and Scientists, Academic Press

**Reference Books:**

- Hoel, Port, and Stone, Introduction to Probability Theory, Publisher: Houghton Mifflin
- Hoel, Port, and Stone, Introduction to Statistical Theory, Publisher: Houghton Mifflin
- W. Feller, An Introduction to Probability Theory and its Applications Volume-I, Third Edition, John Wiley & Sons
- Freedman, Pisani and Purves, Statistics, Viva books; Fourth Edition
- P.L. Meyer, Introductory Probability and Statistical Applications, Oxford and IBH Publishers
- R.E. Walpole and R.H. Myers, Probability & Statistics for Engineers and Scientists, Macmillan
- N. Shiryayev, Probability-1, Springer
- P.Billingsley, Probability and Measure, John Wiley & Sons Inc; 3rd Ed.