Probability Distributions

Paper Code: 
STT 123
Credits: 
5
Contact Hours: 
75.00
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.

 

Students will be able to

Course

Learning outcomes (at course level

Learning and teaching strategies

Assessment Strategies

 

Paper Code

Paper Title

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

 

15.00

Unit-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

 

15.00

Unit –II                                                                                                                    

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

 

15.00

Unit-III                                                                            

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

 

15.00

Unit-IV                                                                                                       

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)

 

15.00

Unit-V                                                                                                             

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: 
  • 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.

 

References: 

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:

 

 

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: 
2022-2023
  • Printer-friendly version
  • PDF version