Probability Distributions

Paper Code: 
STT 201
Credits: 
3
Contact Hours: 
45.00
Max. Marks: 
100.00
Objective: 

This paper is aimed at teaching the students various probability distributions which are useful in day to day life.

 

Students will be able to:

Course

Learning outcomes (at course level

Learning and teaching strategies

Assessment Strategies

 

Paper Code

Paper Title

STT-201

Probability Distributions

CO 15: Learn how to derive the probability distribution function of random variables.

 

CO 16: Obtain the moments from expectation for discrete and continuous probability distribution function.

 

CO 17: Obtain the moments from moment generating function of various discrete and continuous distribution which helps them to study the population deeply.

 

CO 18: Analyse the behaviour of the data by fitting discrete and continuous distributions.

 

CO 19: Identify the descriptive statistics for continuous distributions and learn about their applications.

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

 

9.00
Unit I: 
Random Variable

Definition and types of random variables. Probability mass function and Probability density function. Distribution function with properties (without proof). Joint, Marginal and Conditional probability distributions. Independence of two variables, definition and application of Jacobian transformation for one and two variables.

9.00
Unit II: 
Mathematical Expectations

Expectation of a random variable and its simple properties. Addition and Multiplication theorems of Expectations. Variance and covariance and their properties. Chebychev’s inequality with simple applications.

 

9.00

Central moments and Non-central moments, Moment generating functions and their properties. Cumulant generating functions and their properties

9.00
Unit IV: 
Univariate Discrete Distribution

Bernoulli, Binomial, Poisson, Geometric Distribution with simple properties and applications. Fitting of Binomial and Poisson Distribution. Hypergeometric and Negative Binomial Distribution (examples, derivations, mean and variance) 

9.00
Unit V: 
Univariate Continuous Distribution

Rectangular, Normal, Fitting of Normal, Exponential, Cauchy, Gamma, Beta Distribution with properties

Essential Readings: 

●      Goon, A.M., Gupta, M.K. and Gupta, B. Das (1991): Outline of Statistics, Volume I,   The World Press PvtLtd , Calcutta

●   Gupta, S.C. and Kapoor ,V.K.: (2000) Fundamentals of Mathematical Statistics, S Chand & Company, New Delhi

●        Gupta, O.P.:Mathematical Statistics, Kedarnath Publication, Meerut.

References: 

SUGGESTED READINGS:

 

  • Mood Alexander M., GraybillFrankline and Boes Duane C.:(2007) Introduction to Theory of Statistics, McGraw Hill & Company Third Edition
  • Paul Mayor L. (1970): Introductory Probability and Statistical Application, Oxford & IBM Publishing Company Pvt Ltd, Second Edition.
  • Yule Udny G., and Kendall,M.G. (1999): An Introduction to the theory of Statistics, 14th Edition
  • Speigel M.R., (1967): Theory and Problem of Statistics, Schaum’s Series.
  • Johnson Norman L., Kotz Samuel and Kemp Adriene W.: (2005) Univariate Discrete Distributions, Second 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
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