Probability Theory - Chapter 1

Overview

Beginning my self-study journey into probability theory, working through Chapter 1 of All of Statistics by Larry Wasserman. This chapter covers the foundations of probability including sample spaces, events, and basic probability axioms.

Resources

I’m working through the following resources:

• Primary: All of Statistics by Larry Wasserman, Chapter 1
• Online lectures and problem sets

Key Concepts

Sample Spaces and Events

Sample Space (Ω): The set of all possible outcomes of an experiment.

Event: A subset of the sample space.

Probability Axioms

1. For any event A, P(A) ≥ 0
2. P(Ω) = 1
3. If A₁, A₂, … are disjoint events, then P(⋃ᵢAᵢ) = ∑ᵢP(Aᵢ)

Topics to Explore

• Conditional probability
• Independence
• Bayes’ theorem
• Random variables

Proofs

To be added as I work through the chapter

Examples

To be added as I work through problems

Next Steps

Continue with more detailed examples and practice problems from the textbook.