Course Details:

 

Statistics: Review of statistics, describing data – frequency tables, graphs, and summarizing data – measures of central tendency and variation, multivariate data - correlation coefficient and linear regression. (4 hours)

 

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.  (24 hours)

 

Statistical Inference: Point estimation – maximum likelihood estimation (mle), method of moments, Bayes’ estimator, distributions of sampling statistics, estimation of regression coefficients in a simple linear model, interval estimation, tests of hypotheses – tests for mean and variance, t-test, evaluation of point estimators – unbiasedness, mean squared error (mse), Cramer-Rao bound. (14 hours)


 

Learning Outcomes: Upon successful completion of the course, students will be able to

  1. make probabilistic models for problems arising from physical settings
  2. apply the mathematical tools and results learnt to model for physical problems and draw conclusions in a more precise manner

 

Text/Reference Books:

  1. Robert V. Hogg, Allen Craig, Joseph W. McKean, Introduction to Mathematical Statistics, Pearson, ISBN 978-81-775-8930-6
  2. A. Popoulis and S. Pillai, Probability, Random Variables and Stochastic Processes, McGraw Hill Education; 4 edition, ISBN: 978-0070486584
  3. Sheldon M. Ross, Introduction to Probability and Statistics for Engineers and Scientists, Academic Press, ISBN:978-0-12-370483-2.

 

References :

  1. Hoel, Port, and Stone, Introduction to Probability Theory, Publisher: Houghton Mifflin, ISBN: 978-039504636
  1. Hoel, Port, and Stone, Introduction to Statistical Theory, Publisher: Houghton Mifflin, ISBN: 978-0395046371
  1. W. Feller, An Introduction to Probability Theory and its Applications Volume-I, Third Edition, John Wiley & Sons, ISBN: 978-81-265-1805-0
  1. Freedman, Pisani and Purves, Statistics, Viva books; Fourth Edition, ISBN: 978-8130915876
  1. P.L. Meyer, Introductory Probability and Statistical Applications, Oxford and IBH Publishers, ISBN: 0-201-04710-1.
  2. R.E. Walpole and R.H. Myers, Probability & Statistics for Engineers and Scientists, Macmillan, ISBN: 9788131715529
  3. A. N. Shiryayev, Probability-1, Springer, ISBN: 978-1493979059
  4. P. Billingsley, Probability and Measure, John Wiley & Sons Inc; Third Ed., ISBN: 978-81-265-1771-8