### Probability Theory (MATH-602) (Reg + SS)

The course explores the basic concepts of modern probability theory and its applications for decision-making in economics, business, and other fields of social sciences. Our everyday lives, as well as economic and business activities, are full of uncertainties and probability and distribution theory offer useful techniques for quantifying these uncertainties. The course is heavily oriented towards the formulation of mathematical concepts on probability and probability distributions and densities with practical applications.

Course Objectives:

The course is aimed at:

1. Providing students with a formal treatment of probability theory.
2. To introduce the students to the fundamentals of probability theory and present techniques and basic results of the theory and illustrate these concepts with applications.
3. Fostering understanding through real-world statistical applications.

Learning Outcomes

At the end of the course students should be able to:

1. Develop problem-solving techniques needed to accurately calculate probabilities.
2. Apply problem-solving techniques to solving real-world events.
3. Apply selected probability distributions to solve problems.
4. Present the analysis of derived statistics to all audiences.

Contents

1. Finite probability spaces
2. Basic concept, probability and related frequency
3. Combination of events, examples,
4. Independence, random variables, expected value
5. Standard deviation and Chebyshev's inequality
6. Independence of random variables
7. Multiplicatively of the expected value
9. Discrete Probability Distributions. Probability as a continuous set function
10. Sigma-algebras, examples, Continuous random variables,
11. Expectation and Variance, Normal random variables and Continuous Probability Distributions.
12. Applications: De Moivre-Laplace limit theorem, weak and strong law of large numbers, the Central Limit Theorem, Markov chains and continuous Markov process.

Recommended Books

1. M. Capinski, E. Kopp, Measure, Integral and Probability, (Springer-Verlag, 1998.)

2. R. M. Dudley, Real Analysis and Probability, (Cambridge University Press, 2004.)

Suggested Books

1. S. Ross, A first Course in Probability Theory, 5th ed., (Prentice Hall, 1998.)
2. Robert B. Ash, Basic Probability Theory,( Dover. B, 2008.)

Assessment Criteria

• Sessional: 20 (Assignment 10, Attendance 05, Quiz 05)
• Mid-Term Exam: 30
• Final-Term Exam: 50

Time Table

 Day Time Regular Self-Support Tuesday 08:00 AM to 09:30 AM 11:00 AM to 12:30 PM Friday 08:00 AM to 09:30 AM 11:00 AM to 12:30 PM