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:

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

Reference Books:

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