Everything else is ready: study the parts, the key terms and the quiz below.
- Part 11Turn a recorded fraction into a stated model input
- Part 22One yes-or-no outcome is Bernoulli
- Part 33Ten trials become one binomial count
- Part 44Increase the cohort size, then derive mean and spread
- Part 55Check the model before using its count range
- Part 66Reproduce and challenge the conditional result
Bernoulli and Binomial Outcomes
Model one yes/no outcome and the number of successes in a group.
In this lesson6 parts
- 01Turn a recorded fraction into a stated model input
- 02One yes-or-no outcome is Bernoulli
- 03Ten trials become one binomial count
- 04Increase the cohort size, then derive mean and spread
- 05Check the model before using its count range
- 06Reproduce and challenge the conditional result
Key terms
The words this lesson introduces, each in one line. The module’s glossary collects them all.
- churn indicator
- One for a recorded churn label, zero otherwise.
- parameter p
- The assumed chance of outcome one on one modelled trial; here set to 15.71%.
- Bernoulli trial
- One modelled outcome that is one with probability p and zero otherwise.
- expected value
- Probability-weighted average across possible outcomes.
- variance
- Probability-weighted squared distance from the model mean; p(1 − p) for one Bernoulli trial.
- binomial count
- Number of ones across a fixed number of Bernoulli trials.
- independent
- One trial's outcome does not alter another's probability.
- identically distributed
- Every trial uses the same outcome probabilities.
- binomial distribution
- Probability pattern of the count across a fixed number of independent Bernoulli trials.
- binomial mean
- n times the one-trial probability p.
- standard deviation
- Square root of variance, in the count's units: √(n p (1 − p)).
Quiz 5 questions
Your first pick on each question is the one that counts, and a right one earns a coin. Getting one wrong here is how the lesson sticks.
Practice
Problems to solve in your own notebook. Each states the problem, not the steps: working out the steps is the exercise. Level A applies the lesson, B combines it with earlier ones, C stretches it.
The self-checking notebook for this lesson is Random sampling and count models.
Common mistakes
What you will see when it goes wrong, why it happens, and the fix.
Where it’s used
Where this lesson’s ideas turn up in real work.