Probability Theory

Paper Code: 
STT 122
Credits: 
5
Contact Hours: 
75.00
Max. Marks: 
100.00
Objective: 

Objective: This is a fundamental course in Statistics. This course lays the foundation of probability theory, random variable, probability distribution, mathematical expectation, etc. which forms the basis of basic statistics. The students are also exposed to law of large numbers.

 

Students will be able to

Course

Learning outcomes (at course level

Learning and teaching strategies

Assessment Strategies

 

Paper Code

Paper Title

STT-122

Probability Theory

CO 6: Learn the use of probability theory to solve industry related problems.

 

CO 7: Apply discrete and continuous probability distribution to various practical problems.

 

CO 8: Compute the characteristic functions of some distributions.

 

CO 9: Students will have Deep knowledge about Weak laws and strong laws of large numbers.

 

CO 10: Apply the  various laws of large numbers to sequences of random variables.

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: 
Unit-I

General probability space, various definition of probability, combinations of events, additive and multiplicative law of probability, conditional probability, Bayes’ theorem and its application.

15.00
Unit II: 
Unit-II

Concept of random variable, cumulative distribution function, probability distribution function, joint probability distribution function, marginal distribution function and their application, conditional distribution function and conditional probability distribution function of random variables and their distributions using: jacobian transformation, cumulative distribution function, moment generating function.

15.00
Unit III: 
Unit-III

Mathematical Expectation, moments, Sheppard’s correction, conditional expectation, moment generating function and their applications, cumulant generating function and their applications, characteristic function and its applications. Inversion Theorem, Continuity Theorem, Uniqueness Theorem.

15.00
Unit IV: 
Unit-IV

Levy’s continuity theorem (statement only), probabilities inequalities and their applications, Chebychev inequality, Markov and Jenson inequality. Convergence in probability and convergence in distribution, weak law of large numbers.

15.00
Unit V: 
Unit-V

Central limit theorem: De-Moivre’s Laplace, Liaponouff, Lindeberg-Levy and their simple problems, Zero-One law of Borel and Kolmogorov almost sure convergence in mean square, strong law of large numbers.

Essential Readings: 

● Kingman, J.F. & Taylor, S.J. (1996): Introduction to Measure and Probability, Cambridge Univ. Press.

● Loeve (1996): Probability Theory, Affiliated East –West Press Pvt. Ltd. New Delhi.

● Bhatt, B.R.(2000): Probability, New Age International India.

● Feller,W.(1971): Introduction to Probability Theory and its Applications, Vol. I and II. Wiley, Eastern-Ltd.

● Rohatgi, V.K (1984): An Introduction to Probability Theory and Mathematical Statistics, Wiley Eastern, third edition.

References: 

SUGGESTED READINGS:

 

● Billingsley, P. (1986): Probability and Measure, John Wiley Publications, forth edition.

● Dudley, R.M. (1989): Real Analysis and Probability, Worlds Worth & Books.

● Tucket H.G. (1967): A Graduate Course in Probability, Academic Press.

● Basu, A.K. (1999): Measure Theory and Probability, PHI.

 

e-RESOURCES:

 

· https://epgp.inflibnet.ac.in/

·  https://www.academia.edu/

· https://www.slideshare.net/

· https://www.youtube.com/watch?v=mrCrjeqJv6U&list=PLbMVogVj5nJQWowhOG0-K-...

 

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: 
2023-2024
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