Algebra of Sets: sets and classes, limit of a sequence of sets, rings, sigma-rings, fields, sigma-fields, monotone classes.
Probability: Classical, relative frequency and axiomatic definitions of probability, addition rule and conditional probability, multiplication rule, total probability, Bayes’ Theorem and independence, problems.
Random Variables: Discrete, continuous and mixed random variables, probability mass, probability density and cumulative distribution functions, mathematical expectation, moments, probability and moment generating function, median and quantiles, Markov inequality, Chebyshev’s inequality, problems.
Special Distributions: Discrete uniform, binomial, geometric, negative binomial, hypergeometric, Poisson, continuous uniform, exponential, gamma, Weibull, Pareto, beta, normal, lognormal, inverse Gaussian, Cauchy, double exponential distributions, reliability and hazard rate, reliability of series and parallel systems, problems.
Function of a random variable, problems.
Joint Distributions: Joint, marginal and conditional distributions, product moments, correlation and regression, independence of random variables, bivariate normal distribution, problems.
Transformations: functions of random vectors, distributions of order statistics, distributions of sums of random variables, problems.
Sampling Distributions: The Central Limit Theorem, distributions of the sample mean and the sample variance for a normal population, Chi-Square, t and F distributions, problems.
Descriptive Statistics: Graphical representation, measures of locations and variability.
Estimation: Unbiasedness, consistency, the method of moments and the method of maximum likelihood estimation, confidence intervals for parameters in one sample and two sample problems of normal populations, confidence intervals for proportions, problems.
Testing of Hypotheses: Null and alternative hypotheses, the critical and acceptance regions, two types of error, power of the test, the most powerful test and Neyman-Pearson Fundamental Lemma, tests for one sample and two sample problems for normal populations, tests for proportions, Chi-square goodness of fit test and its applications, problems.

### Course Curriculum

 Algebra of Sets – I Details 54:32 Algebra of Sets – II Details 56:46 Introduction to Probability Details 56:55 Laws of Probability – I Details 54:21 Laws of Probability – II Details 57:53 Problems in Proability Details 58:20 Random Variables Details 54:42 Probability Distributions Details 58:31 Characteristics of Distributions Details 55:46 Special Distributions – I Details 56:1 Special Distributions – II Details 55:47 Special Distributions – III Details 57:6 Special Distributions – IV Details 0:57 Special Distributions – V Details 54:26 Special Distributions – VI Details 56:41 Special Distributions – VII Details 56:13 Function of a Random Variable Details 57:12 Joint Distributions – I Details 54:44 Mod-01Lec-19 Joint Distributions – II Details 59:51 Joint Distributions – III Details 56:35 Joint Distributions – IV Details 54:20 Transformations of Random Vectors Details 56:45 Sampling Distributions – I Details 55:21 Sampling Distributions – II Details 59:28 Descriptive Statistics – I Details 56:26 Descriptive Statistics – II Details 59:26 Estimation – I Details 58:50 Estimation – II Details 56:3 Estimation – III Details 58:2 Estimation – IV Details 57:49 Estimation – V Details 55:12 Estimation – VI Details 56:30 Testing of Hypothesis – I Details 53:59 Testing of Hypothesis – II Details 54:19 Testing of Hypothesis – III Details 57:10 Testing of Hypothesis – IV Details 52:19 Testing of Hypothesis – V Details 54:18 Testing of Hypothesis – VI Details 55:36 Testing of Hypothesis VII Details 55:54 Testing of Hypothesis – VIII Details 56:24

These video tutorials are delivered by IIT Kharagpur as part of NPTEL online courses program.

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