Lecture Details :
Probability and Statistics by Dr.Somesh Kumar,Department of Mathematics,IIT Kharagpur. For more details on NPTEL visit http://nptel.iitm.ac.in
Course Description :
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.
Other Resources :
Other Mathematics Courses
- Numerical Methods and Computation by IIT Delhi
- Foundations of Optimization by IIT Kanpur
- Advanced Matrix Theory and Linear Algebra for Engineers by IISc Bangalore
- Elementary Numerical Analysis by IIT Bombay
- Probability and Random Processes by IIT Kharagpur
- Miscellaneous Mathematics by Other
- Pre-algebra by Khan Academy
- Advanced Complex Analysis Part 1 by IIT Madras
- Computational Techniques by IIT Madras
- Ordinary Differential Equations and Applications by IISc Bangalore
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