Probability
Undergraduate · Math
Syllabus focus
Topics typically covered
Click a topic for the full text and related unit practice.
Undergraduate Probability — scope drawn from Blitzstein & Hwang Introduction to Probability (stat110) open materials and typical calculus-based probability syllabi.
Probability foundations
- Sample spaces and events — Sample spaces and events
- Axioms of probability — Axioms of probability
- Combinatorial probability — Combinatorial probability
- Combinations — Combinations
- Conditional probability and independence — Conditional probability and independence
- Bayes' theorem — Bayes' theorem
- Law of total probability — Law of total probability
Random variables
- Random variables — Random variables
- Continuous — Continuous
- Probability mass functions — Probability mass functions
- Probability density functions — Probability density functions
- Expected value and variance — Expected value and variance
- Standard deviation — Standard deviation
- Joint distributions — Joint distributions
- Conditional distributions — Conditional distributions
- Covariance and correlation — Covariance and correlation
Common distributions and limit theorems
- Common discrete distributions: Bernoulli, binomial, geometric, Poisson — Common discrete distributions: Bernoulli, binomial, geometric, Poisson
- Common continuous distributions: uniform, exponential, normal — Common continuous distributions: uniform, exponential, normal
- Central Limit Theorem (statement) — Central Limit Theorem (statement)
- Normal approximations — Normal approximations
- Sampling distributions (introduction for statistics follow-on) — Sampling distributions (introduction for statistics follow-on)
Study units
Each unit includes a study guide, worksheets, review, practice test, and answer key. One unit is free; subscribe for the full class.
- Probability foundations
Sample spaces and events
Coming soon - Random variables
Random variables
Coming soon - Common distributions and limit theorems
Common discrete distributions: Bernoulli, binomial, geometric, Poisson
Coming soon
Notes
Undergraduate Probability — scope drawn from Blitzstein & Hwang Introduction to Probability (stat110) open materials and typical calculus-based probability syllabi. Topic outline: `content/topics/undergraduate/probability.json`.