Probability, Statistics & Stochastic Processes (MA 501)

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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 (
  • 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


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Lecture #Link of ClassTopic CoveredRemarks
1Class 1: 27 July 2023
2Link is missing.
3Class 3: 1 Aug 2023
4Link is missing.
5Class 5: 4 Aug 2023
6Class 6: 8 Aug 2023Random Variables
7Class 7: 9 Aug 2023Types of Random Variables
8Class 8: 11 Aug 2023CDS
Weekend Doubt clearing Class: 12 Aug 2023
9Class 9: 16 Aug 2023
10Class 10: 18 Aug 2023Inequalities
Weekend Doubt clearing Class: 19 Aug 2023
11Class 11: 22 Aug 2023
12Class 12: 25 Aug 2023
Weekend Doubt clearing Class: 26 Aug 2023
13Class 13: 29 Aug 2023Negative Binomial Diff
14Class 14: 30 Aug 2023
15Class 15: 1 Sep 2023
Weekend Doubt Clearing Class: 2 Sep 2023

Topic wise Learning Material:

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