Probability Theory

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

 

Course

Learning outcomes (at course level

Learning and teaching strategies

Assessment Strategies

Paper Code

Paper Title

STT-122

Probability Theory

CLO 6: Able to apply discrete and continuous probability distribution to various practical problems. 

CLO 7: Deep knowledge about Weak laws and strong laws of large numbers.

CLO 9: Understanding the use of probability theory to solve industry related problems.

CLO 10: Compute the characteristic functions of some distributions.

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

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

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

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

15.00

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

Central limit theorem for a sequence of independent random variables under Linderberg’s condition, central limit theorem of i.i.d. with finite variance, sequence of events and random variables, Zero-One law of Borel and Kolmogorov almost sure convergence in mean square, strong law of large numbers.

 

Essential Readings: 

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

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

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

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

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

6. Billingsley, P. (1986): Probability and Measure, John Wiley Publications.

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

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

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

Academic Year: 
2019-2020
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