Probability Distributions-II

Paper Code: 
24DSTT701
Credits: 
4
Contact Hours: 
60.00
Max. Marks: 
100.00
Objective: 

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.

Course

Course Outcomes

Learning and teaching strategies

Assessment Strategies

Course Code

Course Title

24DSTT701

 

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

 

 

12.00
Unit I: 
Probability Convergence

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

 

12.00
Unit II: 
Compound and Truncated Distributions

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.

 

12.00
Unit III: 
Power Series 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).

 

12.00
Unit IV: 
Multinomial Distributions

Multinomial of binomial and Poisson- moments, moment generating function, cumulant generating function, characteristic functions, recurrence relations, properties, fitting of distributions.

 

12.00
Unit V: 
Advanced 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.

Essential 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.

 

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

 

Academic Year: 
2024-2025
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