MATH 5300 Probability Theory

The course will provide students with a mathematical approach to probability theory based on the theory and methods of real analysis. Starting with the historical development of probability through counting techniques and ratios of outcomes of discrete events, we then proceed to establish the general definition and properties of probability functions. We cover both discrete and continuous probability distributions, moments of random variables and moment generating functions. The course continues on to multivariate probability distributions and functions of random variables. We finish with the development of some famous results in probability theory such as the weak law of large numbers, strong law of large numbers, and central limit theorem.
Credits: 3.0