Reference and Selective Reading
You do not need to read the source books front-to-back for this module. Use the concept pages and practice pages first. Open these local chunks only when you need alternate exposition, more worked examples, or a deeper exercise lane.
Source Roles
| Source | Role | Why it is here |
|---|---|---|
| Introduction to Probability | Primary teaching source | Best overall arc for events, conditioning, random variables, expectation, continuous models, and limit theorems |
| Mathematics for Computer Science | Selective support | Strongest short reinforcements for Bayes, confidence language, random variables, expectation, variance bounds, and sampling |
| Discrete Mathematics and Its Applications | Light support only | Earlier modules already used it for counting foundations; here it is secondary to the dedicated probability texts |
Read Only If Stuck
Probability Models
- Introduction to Probability: Sample spaces and Pebble World
- Introduction to Probability: Naive definition of probability
- Introduction to Probability: How to count (Part 1)
- Introduction to Probability: Non-naive definition of probability (Part 1)
- MCS: Set Theory and Probability
Conditioning, Bayes, and Independence
- Introduction to Probability: Definition and intuition (Part 1)
- Introduction to Probability: Bayes' rule and the law of total probability (Part 1)
- Introduction to Probability: Independence of events (Part 1)
- Introduction to Probability: Conditioning as a problem-solving tool (Part 1)
- Introduction to Probability: Pitfalls and paradoxes (Part 1)
- MCS: The Four-Step Method for Conditional Probability
- MCS: The Law of Total Probability
- MCS: Independence
Random Variables and Distributions
- Introduction to Probability: Random variables
- Introduction to Probability: Distributions and probability mass functions (Part 1)
- Introduction to Probability: Bernoulli and Binomial
- Introduction to Probability: Hypergeometric
- Introduction to Probability: Cumulative distribution functions
- Introduction to Probability: Functions of random variables (Part 1)
- Introduction to Probability: Geometric and Negative Binomial (Part 1)
- Introduction to Probability: Poisson (Part 1)
- MCS: Random Variable Examples
- MCS: Distribution Functions (Part 1)
Expectation, Variance, and Joint Structure
- Introduction to Probability: Definition of expectation
- Introduction to Probability: Linearity of expectation (Part 1)
- Introduction to Probability: Indicator r.v.s and the fundamental bridge (Part 1)
- Introduction to Probability: LOTUS / Variance
- Introduction to Probability: Joint, marginal, and conditional (Part 1)
- Introduction to Probability: 2D LOTUS
- Introduction to Probability: Covariance and correlation (Part 1)
- MCS: Great Expectations (Part 1)
- MCS: Linearity of Expectation (Part 1)
- MCS: Chebyshev's Theorem
Continuous Models and Statistical Thinking
- Introduction to Probability: Probability density functions (Part 1)
- Introduction to Probability: Uniform
- Introduction to Probability: Normal (Part 1)
- Introduction to Probability: Exponential (Part 1)
- Introduction to Probability: Summaries of a distribution (Part 1)
- Introduction to Probability: Law of large numbers
- Introduction to Probability: Central limit theorem (Part 1)
- Introduction to Probability: Sampling and simulation / summary statistics appendix
- MCS: Estimation by Random Sampling
- MCS: Probability versus Confidence (Part 1)
Optional Deep Dive
- Introduction to Probability: Story proofs
- Introduction to Probability: Coherency of Bayes' rule
- Introduction to Probability: Connections between Binomial and Hypergeometric
- Introduction to Probability: Using probability and expectation to prove existence (Part 1)
- Introduction to Probability: Sums of independent r.v.s via MGFs (Part 1)
- Introduction to Probability: Multinomial (Part 1)
- MCS: Markov's Theorem
Concept-to-Source Map
| Primary concept | Best source if stuck | Why this source |
|---|---|---|
| Probability starts with a well-defined model | Introduction to Probability: Sample spaces and Pebble World | Best model-first introduction before formulas appear |
| Conditional probability restricts the world | Introduction to Probability: Definition and intuition (Part 1) | Strongest explanation of conditioning as a reduced sample space |
| Bayes, total probability, and base-rate reasoning | Introduction to Probability: Bayes' rule and the law of total probability (Part 1) | Best blend of derivation and interpretation |
| Random variables turn outcomes into quantities | Introduction to Probability: Random variables | Cleanest bridge from events to quantities |
| Core discrete distribution families | Introduction to Probability: Bernoulli and Binomial | Strong anchor for the family-model viewpoint |
| Expectation is the center of a random process | Introduction to Probability: Definition of expectation | Most direct explanation of weighted averages |
| Linearity and indicator variables are the main workhorses | Introduction to Probability: Indicator r.v.s and the fundamental bridge (Part 1) | Best route from counting questions to expectation tricks |
| Variance, joint structure, and covariance | Introduction to Probability: Covariance and correlation (Part 1) | Clear explanation of how dependence enters spread calculations |
| Continuous random variables use densities, not point masses | Introduction to Probability: Probability density functions (Part 1) | Best first explanation of density versus probability |
| Averages, simulation, and confidence language | MCS: Estimation by Random Sampling | Best short bridge from probability theory to statistical interpretation |