Course Description
Objective: This course will focus on strengthening foundation of probability keeping its application into signal processing and communications in mind. The course is divided into two parts. First part would discuss probability space, random variables and their transformations, conditional distributions and estimation of random variables. Second part will extend the theory to random vectors, random processes including Markov chains and some applications into linear systems. After completion of the course, the students should be able to strengthen their base in probability theory and stochastic processes and apply these tools in their own research.
Course Content
- Introduction to Probability
- Review of set theory, real analysis
- Cardinality and Countability
- Probability Space
- Discreet Probability space
- Continuous Probability space
- Conditional Probability and Independence
- Random Variable
- Continuous and Discreet Random Variable
- Distribution: CDF and PDF/PMF
- Random Variable Transformation
- Functions of Random Variables
- Measures of Random Variable: Expectation, Variance
- Conditional Expectation
- Characteristic functions, Laplace, MGF
- Convergence of RVs, Law of Large Number, CLT
- Concentration Inequalities
- Random Process
- Examples
- Measures of Random Process
- Properties of Random Process
- Discreet time markov chain (DTMC)