Probability Distributions

Paper Code: 
24STT123
Credits: 
6
Contact Hours: 
90.00
Max. Marks: 
100.00
Objective: 

This course lays the foundation of probability distributions and sampling distributions, their application which forms the basis of Statistical Inference.

 

Course Outcomes: 

Course

Course Outcomes

Learning and teaching strategies

Assessment Strategies

Course Code

Course Title

24STT123

Probability Distributions

(Theory)

CO 13: Identify the behavior of the discrete population and sample and their distribution and apply it on real world problems.

CO 14: Identify the behavior of the population and apply it on multiple variables problems.

CO 15:  Derive the continuous probability distributions of random variables and use these techniques to differentiate data and fit in real life scenarios.

CO 16: Translate real-world sample problems into probability distributions and give an appropriate inference.

 CO 17: Analyze the behavior of the data and apply the appropriate test.

CO 18: 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.

Classroom Quiz,

Assignments,

Class Test,

Individual Presentation.

 

18.00
Unit I: 
Discrete Distributions-I

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.

 

18.00
Unit II: 
Discrete Distributions-II

Geometric distribution, Negative Binomial distribution, Hyper-geometric distributions, Power Series distribution- moments, moment generating function, cumulant generating function, characteristic functions, recurrence relations, properties, fitting of distributions.

 

18.00
Unit III: 
Continuous Distributions-I

Rectangular distribution, Normal distribution (truncated also), normal probability plot, Exponential distribution, Lognormal distribution, Multinomial of binomial and Poisson- moments, moment generating function, cummulant generating function, characteristic functions, recurrence relations, properties, fitting of distributions.

 

18.00
Unit IV: 
Continuous Distributions-II

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).

 

18.00
Unit V: 
Sampling Distributions

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.

 

Essential Readings: 

ESSENTIAL READINGS: 

·        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/

·        https://www.academia.edu/

·        https://www.slideshare.net/

 

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

 

Academic Year: 
2024-2025
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