The course aims to teach the students the fundamental concepts in probability theory and random processes. The goal is to develop skills to use conditional probability, random variables, discrete and continuous probability distributions. The course also aims to teach expectation, variance, and moment generating functions.
Upon successful completion of this course, students will be able to
1. Recall notation, conventions, definitions, theorems and certain examples related to the probability theory,
2. Determine the mean and variance of a random variable,
3. Recognize the general properties of expectation and variance operators,
4. Compute probabilities by modeling sample spaces,
5. Apply the rules of additive and multiplicative laws, permutations, combinations, and conditional probability,
6. Interpret the fundamental axioms and rules in probability: Bayes’ Theorem, Central Limit Theorem, Law of Total Probability and Conditional Expectation,
7. Describe the main properties of probability distributions and random variables,
8. Identify the random variables of interest in a given scenario.