Probability Distributions-I

Paper Code: 
24CSTT201
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.

Course

Course Outcomes

Learning and teaching strategies

Assessment Strategies

Course Code

Course Title

24CSTT201

Probability Distributions-I (Theory)

CO 12: Identify the behavior of the population and modify it.

CO 13: Acquire the skill to obtain the various constants using expectation. 

CO 14: Obtain the moments from moment generating function of various discrete and continuous distributions which helps them to study the population deeply.

CO 15:  Conduct an in-depth examination of data behavior through the application of discrete distributions.

CO 16: Examine and differentiate the continuous population and apply on the appropriate distribution.

CO 17: 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.

Classroom Quiz,

Assignments,

Class Test,

Individual Presentation.

 

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: 
Mathematical Expectation

Expectation of a random variable and its simple properties. Addition and Multiplication theorems of Expectations. Variance and covariance and their properties with simple problems.

 

12.00
Unit III: 
Moments

Central moments and Non-central moments, skewness, kurtosis. Moment generating functions and their properties. Cumulant generating functions. Chebychev’s inequality (without proof) with simple applications.

 

12.00
Unit IV: 
Univariate Discrete Distribution

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

 

 

12.00
Unit V: 
Univariate Continuous Distribution

Rectangular, Normal distribution, Central limit theorem (CLT) for i.i.d. variates (without proof) and simple questions. 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.

 

SUGGESTED READINGS: 

  • Mood Alexander M., Graybill Frankline 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

       

 

Academic Year: 
2024-2025
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