Probabilistic Systems Analysis and Applied Probability

Unit I: Probability Models And Discrete Random Variables

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This unit covers the basic framework of probability theory: probabilistic models, conditional probabilities, independence, the Bayes’ rule, and counting methods. In addition, it introduces discrete random variables and the concept of the Probability Mass Function (PMF) used to describe the probability distribution of one or several random variables. Finally, it defines the concepts of expectation and variance, and their basic properties.

Lecture 1: Probability Models and Axioms

Lecture 2: Conditioning and Bayes’ Rule

Lecture 3: Independence

Lecture 4: Counting

Lecture 5: Discrete Random Variables; Probability Mass Functions; Expectations

Lecture 6: Discrete Random Variable Examples; Joint PMFs

Lecture 7: Multiple Discrete Random Variables

Quiz 1

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