Bernoulli trials and the binomial distribution: probabilities, mean np and variance np(1 - p)

What this note covers

1. One trial: the Bernoulli variable
2. When a count is binomial
3. Exactly k successes and the combinations factor
4. Cumulative events, complements and discrete boundaries
5. Mean and spread of the success count
6. Solving backwards for a trial count or probability
7. Connected reasoning across Bernoulli distributions / Binomial distributions
8. Error analysis and final checks for Bernoulli distributions / Binomial distributions

8 sections · 10 key terms & formulas · 6 common mistakes