Study Guide — Common distributions and limit theorems
Probability
Undergraduate study guide for Common distributions and limit theorems.
What this standard means
- Common discrete distributions: Bernoulli, binomial, geometric, Poisson
- Common continuous distributions: uniform, exponential, normal
- Central Limit Theorem (statement) and normal approximations
- Sampling distributions (introduction for statistics follow-on)
_See printable PDF for diagram._
How to use the 20 practice sets
| Sets | When to use | | --- | --- | | 1–5 | Intro — explore together, short written items | | 6–10 | Core skills — diagrams and written practice | | 11–15 | Mixed review — explain thinking | | 16–20 | Stretch — word problems and mastery tasks |
Pacing: 10–15 minutes per session.
How to practice
1. Draw a probability table or tree 2. Check probabilities sum to 1 3. Name the distribution before computing
_See printable PDF for diagram._
Common mistakes
- Assuming independence without justification
- Confusing P(A|B) and P(B|A)
Review and practice tests
1. Start Review 1/10 when sets 1–3 feel comfortable. 2. Move up one review level with little help. 3. Use Practice Test 4/10–6/10 for mid-standard checks. 4. Practice Test 10/10 is the mastery bar for Common distributions and limit theorems.
- [ ] Computes probabilities from models
- [ ] Finds expectation and variance
- [ ] Chooses appropriate distributions
Materials for this standard
- Practice Problems — 20 printable sets
- Review — 10 difficulty levels
- Practice Test — 10 difficulty levels
- Answer key — for parents and tutors