### MA5400 Probability Theory

#### Course Details

Probability: Axiomatic Definitions, Three Definitions of Probability, Independent Events, Arithmetical Density, Counting and Probability.

Random Variables, Distributions and Expectations, Discrete and Continuous Random Variables, Borel Fields and General Random Variables.

Conditioning and Independence, Sequential Sampling, Mean Variance and Transforms.

Poisson Process, Law of Large Numbers, Central Limit Theorem, Stirling's Formula and De-Moivre's Theorem.

Introduction to Random Walk, Markov Chain and Martingale

#### Course References:

Text Books:

1. K. L. Chung and F. AitSahlia, Elementary probability theory, fourth edition, Undergraduate Texts in
Mathematics, Springer-Verlag, New York, 2003.

Reference Books:

1. Feller, William. An Introduction to Probability Theory and its Applications. Vol. I and II. New York,
NY: Wiley, 1968-1971.

2. Jacod, Jean; Protter, Philip. Probability essentials. Second edition. Universitext. Springer-Verlag,
Berlin, 2003.

3. Walsh John B. Knowing the Odds: An Introduction to Probability. American Mathematical Soc.
2012.

4. Dudley, R. M. Real Analysis and Probability. Cambridge, UK: Cambridge University Press, 2002.