Discrete distributions: Bernoulli, binomial, Poisson
The normal distribution describes measured quantities — height, weight, time. But a huge share of an analyst's data is COUNTS: clicked or not, how many purchases, how many errors per hour. Count data has its own distributions. Let's cover the main three — and where each shows up. Press "pour": a real sample's histogram settles onto the theoretical PMF.
PMF — probability mass: bar height = the probability of exactly that value. Bars sum to 1.
One trial with two outcomes, "success/failure": bought / did not, heads / tails, clicked / not. The single parameter p is the success probability (bar heights p and 1−p). The brick from which the binomial and A/B conversion shares are built. Press "pour" — the real sample\'s histogram approaches the theoretical PMF.
The list at the top of the widget offers three discrete distributions. Start with the simplest yes/no experiment: clicked / did not, bought / did not, heads / tails. That is the Bernoulli distribution (selected by default): just two bars whose heights are p and 1−p. Drag p — the weight flows between "yes" and "no". This is the brick almost everything else is built from.
For an analyst this is not an abstraction but a daily tool. Conversion (bought / did not) is Bernoulli per user and binomial per group; that is why confidence intervals for A/B conversion are computed under the binomial model.
Poisson describes load and streams: how many requests per second, how many support tickets per day, how many defects per batch. Knowing λ you can estimate the chance of overload and plan capacity.
Insurers and call centers plan resources with Poisson: the average number of events is known, and the distribution prices the "peak days".
Quality control counts defects per batch (Poisson/binomial) and decides when to sound the alarm. And any "share"-type metric is binomial at heart.