Probability Theory

Prerequisite(s): Statistics

Credit Hours: 3+0

Objectives of the course:

A prime objective of the course is 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. This course will also present the basic principles of random variables and random processes needed in 24 applications.

Course Contents:

Finite probability spaces: Basic concept, probability and related frequency, combination of events, examples, independence, random variables, expected value, standard deviation and Chebyshev's inequality, independence of random variables, multiplicatively of the expected value, additivity of the variance, discrete probability distribution.Probability as a continuous set function: Sigma-algebras, examples, continuous random variables, expectation and variance, normal random variables and continuous probability distribution.

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

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

3. Resnick S. I., A Probability Path, Birkhauser, 1999.

4. Ross S. A first Course in Probability Theory, 5th ed., Prentice Hall, 1998.

5. Robert B. Ash, Basic Probability Theory, Dover. B, 2008.

6. Chaudhry, S.M. and Kamal, S. (2008), Introduction to Statistical Theory, Part I, II,

8th ed, Ilmi Kitab Khana, Lahore, Pakistan.