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Probability Distributions
Objective: This course lays the foundation of probability distributions and sampling distributions, their application which forms the basis of Statistical Inference.
Students will be able to
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Assessment Strategies
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STT-123 |
Probability Distributions |
CO 11: Identify the behavior of the discrete population and sample and their distribution.
CO 12: Derive the probability distributions function of random variables and use these techniques to generate data from various distributions.
CO 13: Identify the behavior of the continuous population and sample and their distribution.
CO 14: Analyse the behaviour of the data by Fitting the discrete and continuous distributions.
CO 15: Translate real-world sample problems into probability distributions and give an appropriate inference. |
Approach in teaching: Interactive Lectures, Group Discussion, Classroom Assignment Problem Solving Sessions
Learning activities for the students: Assignments Seminar Presentation Subject based Activities |
Classroom Quiz Assignments Class Test Individual Presentation |
Bernoulli distribution, Binomial distribution (compound and truncated also), Poisson distribution (compound and truncated also)- moments, moment generating function, Cumulant generating function, characteristic functions, recurrence relations, properties, fitting of distributions
Geometric distribution, Negative Binomial distribution, Hyper-geometric distributions, Power Series distribution- moments, moment generating function, cummulant generating function, characteristic functions, recurrence relations, properties, fitting of distributions
Rectangular distribution, Normal distribution (truncated also), Exponential distribution, Lognormal distribution, Multinomial of binomial and Poisson- moments, moment generating function, cummulant generating function, characteristic functions, recurrence relations, properties, fitting of distributions
Triangular distribution, Gamma distribution (one and two parameter) , Beta distribution( I kind and II kind) Cauchy distribution (truncated also), Laplace distributions, Pearson’s distribution (Type I, IV and VI)
Chi-Square, t and F distributions (central and non-central) and their applications. Large sample test. Fisher’s Z 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.
● Goon, Gupta & Das Gupta. (2003): Outline of Statistical Theory. Vol. I, World Press.
● Hogg, R.V. and Craig, A.T.(2009): Introduction to Mathematical Statistics, McMillan.
● Johnson, S. and Kotz. (1972): Distribution in Statistics, Vol.I, II. And III, Houghton and Muffin.
SUGGESTED READINGS:
● 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.
● Rohatgi, V.K. (1984): An Introduction to Probability Theory and Mathematical Statistics, Wiley Eastern, third edition.
e-RESOURCES:
· https://epgp.inflibnet.ac.in/
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
