Probability Distributions (Theory)

Paper Code: 
24GBDA201
Credits: 
04
Periods/week: 
04
Max. Marks: 
100.00
Objective: 

This module enables students to

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

 

Course Outcomes: 

Course

Learning outcome

(at course level)

Learning and teaching strategies

Assessment Strategies

Course Code

Course

Title

24GBDA 201

Probability Distributions

(Theory)

 

CO85. Create random variables and apply their functions in real world scenario.

CO86. Infer the expectations for random variable functions.

CO87. Compute the moments and characteristic functions of distributions.

CO88. Identify the behaviour of the population.

CO89. Analyse the behaviour of the data by fitting discrete and continuous distributions.

CO90. Contribute effectively in course-specific interaction

Approach in teaching: Interactive Lectures, Discussion, Reading assignments, Demonstration.

 

Learning activities for the students: Self learning assignments, Effective questions, Seminar presentation.

Class test,

Semester end examinations,

Quiz,

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:

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: 
Cumulant generating functions:

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

 

12.00
Unit IV: 
Probability Distribution-I:

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

 

12.00
Unit V: 
Probability Distribution-II:

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

 

ESSENTIAL READINGS: 

SUGGESTED TEXT BOOKS

  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: 

SUGGESTED REFERENCE BOOKS

  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:

  1. Probability, Academia: https://www.academia.edu/39708554/Probability_and_Statistics_for_Data_Science
  2. Probability ,slide share:  https://www.slideshare.net/ferdinjoe/probability-theory-for-data-scientists-     193754474?from_search=0

 

JOURNALS:

  1. Journal of Machine Learning Research (JMLR),ACM, https://dl.acm.org/journal/jmlr

 

Academic Year: 
2024-25
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