EN.553.211 · Zan Ahmad · September 30, 2026
One trial.
Four count models.
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47 explanations · foundations, examples, and formulas
One trial → binomial → Skittles → rain
83 explanations · counting, proofs, and simulations
Includes Pascal’s triangle and both limiting models
Resume Wednesday at the cereal example →
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Detailed sections
- One trial → a count
- Count the arrangements
- Pascal → binomial theorem
- Finish the cereal example
- Binomial moments
- Why independence changes the variance
- Change the sampling rule
- Skittles: count without replacement
- Same chance before seeing the draws
- Dependence appears in the variance
- A large population approaches replacement
- Many tiny chances → an event count
- Derive the Poisson limit
- Prove the Poisson formulas
- Use the model, then compare
- Further review: infer a Poisson parameter
The short version follows the requested class and test-review scope. It is not a claim about the final exam’s question selection. Simulations estimate frequencies; the exact laws and the proofs explain the limits.