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Probability Distributions-II
This paper is aimed at teaching the students various probability distributions which are useful in day to day life and able to obtain the probabilities when sample size is large.
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Course |
Course Outcomes |
Learning and teaching strategies |
Assessment Strategies |
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Course Code |
Course Title |
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24DSTT701
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Probability Distributions-II (Theory) |
CO 89: Identify the behavior of the discrete population and sample and their distribution. CO 90: Derive the continuous probability distributions of random variables and use these techniques to differentiate data and fit in real life scenario. CO 91: Identify the behavior of the population having multiple variables and their distribution. CO 92: Analyze the behavior of the data and apply the appropriate test. CO 93: Translate real-world sample problems into probability distributions and give an appropriate inference. CO 94: Contribute effectively in course-specific interaction. |
Approach in teaching: Interactive Lectures, Group Discussion, Classroom Assignment Problem Solving Sessions
Learning activities for the students: Assignments Seminar Presentation Subject based Activities |
Software based Assignments Individual Presentation Class Test |
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
Compound Binomial distribution, Compound Poisson distribution - moments, moment generating function, Cumulant generating function, recurrence relations, properties, truncated binomial distribution, truncated Poisson distribution, Truncated Normal distribution.
Power Series distribution- moments, moment generating function, cumulant generating function, characteristic functions, recurrence relations, properties, fitting of distributions, Lognormal distribution, Triangular distribution, Cauchy distribution (truncated also).
Multinomial of binomial and Poisson- moments, moment generating function, cumulant generating function, characteristic functions, recurrence relations, properties, fitting of distributions.
Non central Chi-Square, t and F distributions and their applications. Order statistics: their distributions and properties; joint and marginal distributions of order statistics, sampling distributions of range and median of univariate population.
- Kendall, M.G. and Stuart. (1996): An Advanced Theory of Statistics, Vol. I,II. Charls Griffin.
- Mood,A.M., Graybill, F.A. and Boes, D.C.(2007): Introduction to the Theory of Statistics, McGraw Hill, third edition.
- Mukhopadhyay, P. (1996): Mathematical Statistics, New Central Book Agency (P) Ltd.
SUGGESTED READINGS:
- Rohatgi, V.K. (1984): An Introduction to Probability Theory and Mathematical Statistics, Wiley Eastern, third edition.
- 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.
- Tucket H.G. (1967): A Graduate Course in Probability, Academic Press.
- Basu, A.K. (1999): Measure Theory and Probability, PHI.
e-RESOURCES:
JOURNALS:
- Sankhya The Indian Journal of Statistics, Indian Statistical Institute
- Aligarh Journal of Statistics, Department of Statistics and Operations Research, Aligarh Muslim University
- Afrika Statistika, Saint-Louis Senega University
- International Journal of Statistics and Reliability Engineering, Indian Association for Reliability and Statistic
- Journal of the Indian Society for Probability and Statistics, Indian Society for Probability and Statistics
- Journal of the Indian Statistical Association, Indian Statistical Association
- Statistica, Department of Statistical Sciences Paolo Fortunato, University of Bologna
- Statistics and Applications, Society of Statistics, Computer and Applications
- Stochastic Modeling and Applications, MUK Publications and Distributions
