Fundamentals of Probability course provides a formal and systematic introduction to probability and probabilistic models.
The course will introduce the concepts of finite probability theory, continuous probability theory and random processes. Students are expected to gain an understanding and skills in problem solving related to sample spaces, random variables, expectations, transforms, Bernoulli and Poisson processes, finite Markov chains and limit theorems.
| Week | Topic |
|---|---|
| 1 | Introduction to probability.Random experiments, sample spaces and events. Axioms of probability. |
| 2 | Conditional probability. Multiplication and total probability rules. Independence. Bayes rule. |
| 3 | Discrete random variables. Probability mass function & cumulative distribution functions. Mean and variance. |
| 4 | Probability distributions: uniform, binomial and geometric distributions. Their mean and variance. |
| 5 | Probability distributions: negative binomial, hypergeometric and Poisson distributions |
| 6 | Continuous random variables. Probability density functions and cumulative distribution functions. Mean and variance. |
| 7 | Midterm exam. |
| 8 | Continuous probability distributions. The uniform and normal distribution. |
| 9 | The exponential distribution. Overview of lognormal, Erlang, Gamma and Weibull probability distributions. |
| 10 | Joint Distributions |
| 11 | Expectation for Multivariate Distribution |
| 12 | The Bernoulli and Poisson Processes |
| 13 | Markov Chains |
| 14 | Overview in general |
| Method | % Each | Quantity |
|---|---|---|
| Midterm Exam(s) | 35 | 1 |
| Quiz | 7.5 | 2 |
| Final Exam | 45 | 1 |
| Attendance | 5 |
D. Montgomery, G.Runger «Applied Statistics and Probability for Engineers»