Standard syllabus
Probability · Undergraduate · Math
Learning objectives from the Probability syllabus, grouped by unit. Click an objective for study materials.
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)
Learning objectives
Click an objective for study materials.
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
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)
Multi-Unit Problems
Course-level sets that combine skills across study units (coming soon).
Browse Multi-Unit ProblemsWhat each unit includes
Open a unit below for full materials. Typical resources:
- Study guide
- Exam Strategy
- Common Mistakes
- Worksheets
- Word problems
- Mixed Practice
- Multi-Unit Problems
- Review
- Practice test
- Answer key
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
Pricing calculator
Choose materials, tutoring, or both — or book a single session as needed. Customize your plan on the subscribe page.
$1,162 · Probability · 18 tutoring hrs
Study guides, worksheets, reviews, practice tests, and answer keys for 1 class. 18 tutoring hours (1 hr / week · semester). Bundle discount applied vs buying separately. Pay in full via Zelle.