Coming soon
Probability Theory
This is a fundamental course in Statistics. This course lays the foundation of probability theory, random variable, probability distribution, mathematical expectation, etc. which forms the basis of basic statistics. The students are also exposed to law of large numbers
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Course |
Learning outcomes (at course level) |
Learning and teaching strategies |
Assessment Strategies |
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Paper Code |
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STT122 |
Probability Theory (Theory)
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The students will be able to –
CO6: Able to apply discrete and continuous probability distribution to various practical problems. CO7: Deep knowledge about Weak laws and strong laws of large numbers. CO8: Able to deal with the applications of law of large numbers. CO9: Understanding the use of probability theory to solve industry related problems. CO10: Compute the characteristic functions of some distributions. |
Approach in teaching:
Interactive Lectures, Discussion, Power Point Presentations, Informative videos
Learning activities for the students: Self learning assignments, Effective questions, presentations, Field trips
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Quiz, Poster Presentations, Power Point Presentations, Individual and group projects, Open Book Test, Semester End Examination
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General probability space, various definition of probability, combinations of events, additive and multiplicative law of probability, conditional probability, Bayes’ theorem and its application.
Concept of random variable, cumulative distribution function, probability distribution function, joint probability distribution function, marginal distribution function and their application, conditional distribution function and conditional probability distribution function of random variables and their distributions using: jacobian transformation, cumulative distribution function, moment generating function.
Mathematical Expectation, moments, Sheppard’s correction, conditional expectation, moment generating function and their applications, cumulant generating function and their applications, characteristic function and its applications. Inversion Theorem, Continuity Theorem, Uniqueness Theorem.
Levy’s continuity theorem (statement only), probabilities inequalities and their applications, Chebychev inequality, Markov and Jenson inequality. Convergence in probability and convergence in distribution, weak law of large numbers,
Central limit theorem: De-Moivre’s Laplace, Liaponouff, Lindeberg-Levy and their simple problems, Zero-One law of Borel and Kolmogorov almost sure convergence in mean square, strong law of large numbers.
BOOKS RECOMMENDED
- Kingman, J.F. & Taylor, S.J. (1996): Introduction to Measure and Probability, Cambridge Univ. Press.
- Loeve (1996): Probability Theory, Affiliated East –West Press Pvt. Ltd. New Delhi.
- Bhatt, B.R. (2000): Probability, New Age International India.
- Feller,W.(1971): Introduction to Probability Theory and its Applications, Vol. I and II. Wiley, Eastern-Ltd.
- Rohatgi, V.K (1984): An Introduction to Probability Theory and Mathematical Statistics, Wiley Eastern, third edition.
- Billingsley, P. (1986): Probability and Measure, John Wiley Publications, forth edition.
- Dudley, R.M. (1989): Real Analysis and Probability, Worlds Worth & Books.
- Tucket H.G. (1967): A Graduate Course in Probability, Academic Press.
- Basu, A.K. (1999): Measure Theory and Probability, PHI.
