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Syllabus
Algebra of sets, probability spaces, random variables, cumulative distribution functions, mathematical expectations, conditional probability and expectation, moments and inequalities, special discrete and continuous probability distributions, function of a random variable, random vectors and their distributions, convolutions, joint, marginal and conditional distributions, product moments, independence of random variables, bivariate distributions and properties, order statistics and their distributions, sampling distributions, Central Limit Theorem, strong law of large numbers, sequence of random variables, modes of convergence, distributions of the sample mean and the sample variance for a normal population, chi-square, t and F distributions, method of moments and maximum likelihood estimation, concepts of unbiasedness, criteria for choosing estimators, consistency and efficiency of estimates, confidence intervals, pivotal quantities, confidence intervals for proportions, simple and composite hypothesis, null and alternative hypotheses, types of error, level and size of tests, the most powerful test and Neyman – Pearson Fundamental Lemma, tests for one- and two-sample problems for normal populations, tests for proportions, likelihood ratio tests, chi-sqaure test for goodness of fit. discrete and continuous stochastic processes, markov chains, transition probability matrix, state spaces, classification of states, stationary distributions, ergodicity, poisson process, birth and death process
Reference Books:
- Rohatgi, V.K., and Saleh, A.K.Md. Ehsanes (2009).An introduction to probability and statistics. Second Edition, Wiley India.
An Introduction to Probability and Statistics (usb.ac.ir) - Introduction to the Theory of Statistics; Alexander M. Mood, Franklin A. Graybill, Duane C. Boes, Tata McGraw Hill.
- Milton, J.S. and Arnold, J.C. (2009) Introduction to Probability and Statistics, Fourth Edition, Tata Mcgraw-Hill.
- Ross, S.M.(2008) Introduction to Probability Models, Ninth edition, Academis Press.
- Statistical Inference (2007), G. Casella and R.L. Berger, Duxbury Advanced Series
Classes
(You may need to login into IITP LMS for some classes. Better to login in one tab and then access these resources)
| Lecture # | Link of Class | Topic Covered | Remarks |
|---|---|---|---|
| 1 | Class 1: 27 July 2023 | ||
| 2 | Link is missing. | ||
| 3 | Class 3: 1 Aug 2023 | ||
| 4 | Link is missing. | ||
| 5 | Class 5: 4 Aug 2023 | ||
| 6 | Class 6: 8 Aug 2023 | Random Variables | |
| 7 | Class 7: 9 Aug 2023 | Types of Random Variables | |
| 8 | Class 8: 11 Aug 2023 | CDS | |
| Weekend Doubt clearing Class: 12 Aug 2023 | |||
| 9 | Class 9: 16 Aug 2023 | ||
| 10 | Class 10: 18 Aug 2023 | Inequalities | |
| Weekend Doubt clearing Class: 19 Aug 2023 | |||
| 11 | Class 11: 22 Aug 2023 | ||
| 12 | Class 12: 25 Aug 2023 | ||
| Weekend Doubt clearing Class: 26 Aug 2023 | |||
| 13 | Class 13: 29 Aug 2023 | Negative Binomial Diff | |
| 14 | Class 14: 30 Aug 2023 | ||
| 15 | Class 15: 1 Sep 2023 | ||
| Weekend Doubt Clearing Class: 2 Sep 2023 |
Topic wise Learning Material:
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