PROBABILITY DISTRIBUTIONS

Paper Code: 
GBDA 201
Credits: 
4
Periods/week: 
4
Max. Marks: 
100.00
Objective: 

This module enables students to

  1. Understand Random Variable Concepts.
  2. Learn Fundamental of Probability Distribution.

Course Outcomes (COs).

Course Outcome (at course level)

 

Learning and teaching strategies

Assessment Strategies

On completion of this course, the students will:

CO72. Demonstrate the random variables and its functions.

CO73. Infer the expectations for random variable functions.

CO74. Compute the moments and characteristic functions of distributions.

CO75. Identify the behaviour of the population.

CO76.Analyse the behaviour of the data by fitting discrete and continuous distributions.

Approach in teaching:

Interactive Lectures, Discussion, Tutorials, Reading assignments, Demonstrations.

  • Class test
  • Semester end examinations
  • Quiz
  • Solving problems in tutorials
  • Assignments
  • Presentations
  • Individual and group projects and peer reviews
 

 

12.00
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.

 

12.00
Unit II: 

Expectation of a random variable and its simple properties. Addition and Multiplication theorems of Expectations. Variance and covariance and their properties. Central moments and Non-central moments and their computation from data. Measure of Skewness and Kurtosis.

 

12.00
Unit III: 

Chebychev’s inequality with simple applications. Moment generating functions and their properties. Cumulant generating functions. Characteristic function and their properties (without proof)

 

12.00

Binomial, Poisson, Geometric Distribution with simple properties and applications.

 

12.00
Unit V: 

Uniform Distribution, Normal Distribution, Properties of Normal Curve, and Exponential Distribution with properties.

 

ESSENTIAL READINGS: 
  1. Goon, A.M., Gupta, M.K. and Gupta, B. Das (1991): Outline of Statistics, Volume I, The World Press PvtLtd , Calcutta  
  2. Gupta, S.C. and Kapoor ,V.K.: (2000) Fundamentals of Mathematical Statistics, S Chand & Company, New Delhi
  3. Gupta, O.P.:Mathematical Statistics, Kedarnath Publication, Meerut.
  4. Mood Alexander M., GraybillFrankline and Boes Duane C.:(2007) Introduction to Theory of Statistics, McGraw Hill & Company Third Edition

 

REFERENCES: 
  1. Paul Mayor L. (1970): Introductory Probability and Statistical Application, Oxford & IBM Publishing Company Pvt Ltd, Second Edition.
  2. Yule Udny G., and Kendall,M.G. (1999): An Introduction to the theory of Statistics,14th Edition
  3. Speigel M.R., (1967): Theory and Problem of Statistics, Schaum’s Series.
  4. Johnson Norman L., Kotz Samuel and Kemp Adriene W.: (2005) Univariate Discrete Distributions, Second Edition.
  5. Kingman, J.F. & Taylor, S.J. (1996): Introduction to Measure and Probability, Cambridge Univ. Press.
  6. Johnson, S. and Kotz. (1972): Distribution in Statistics, Vol.I, II. And III, Houghton and Muffin.

 

E-RESOURCES:

JOURNALS:

 

 

 

Academic Year: 
2022-23
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