IIT Kharagpur Course , Prof. Somesh Kumar

**432**students enrolled

IIT Kharagpur Course , Prof. Somesh Kumar

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, Chebyshevs 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.

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, Chebyshevs 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.

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3.2 (67 Ratings)

Probability and Statistics by Dr.Somesh Kumar,Department of Mathematics,IIT Kharagpur. For more details on NPTEL visit httpnptel.iitm.ac.in

31%

18%

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24%

- 1.Algebra of Sets - I
- 2.Algebra of Sets - II
- 3.Introduction to Probability
- 4.Laws of Probability - I
- 5.Laws of Probability - II
- 6.Problems in Proability
- 7.Random Variables
- 8.Probability Distributions
- 9.Characteristics of Distributions
- 10.Special Distributions - I
- 11.Special Distributions - II
- 12.Special Distributions - III
- 13.Special Distributions - IV
- 14.Special Distributions - V
- 15.Special Distributions - VI
- 16.Special Distributions - VII
- 17.Function of a Random Variable
- 18.Joint Distributions - I
- 19.Mod-01Lec-19 Joint Distributions - II
- 20.Joint Distributions - III
- 21.Joint Distributions - IV
- 22.Transformations of Random Vectors
- 23.Sampling Distributions - I
- 24.Sampling Distributions - II
- 25.Descriptive Statistics - I
- 26.Descriptive Statistics - II
- 27.Estimation - I
- 28.Estimation - II
- 29.Estimation - III
- 30.Estimation - IV
- 31.Estimation - V
- 32.Estimation - VI
- 33.Testing of Hypothesis - I
- 34.Testing of Hypothesis - II
- 35.Testing of Hypothesis - III
- 36.Testing of Hypothesis - IV
- 37.Testing of Hypothesis - V
- 38.Testing of Hypothesis - VI
- 39.Testing of Hypothesis VII
- 40.Testing of Hypothesis - VIII

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