Probability Distributions
The handful of named distributions (normal, binomial, Poisson) that show up repeatedly, and what each models.
Discrete vs. continuous
A discrete distribution assigns probability to specific countable outcomes (e.g. number of heads in 10 coin flips); a continuous distribution assigns probability density over a range of real numbers (e.g. height), where probability of any exact single value is technically zero.
The recurring few
- Normal (Gaussian) — the symmetric bell curve, fully described by mean and variance; the Central Limit Theorem is why it shows up everywhere (sums/averages of many independent random variables tend toward normal, regardless of the underlying distribution).
- Binomial — number of successes in n independent yes/no trials with fixed success probability p.
- Poisson — number of events in a fixed interval, given a constant average rate — the standard model for "how many arrivals per hour."
Why it matters
Knowing which distribution models your data determines which statistical tests are valid — many classical tests (t-test, ANOVA) assume approximately normal data, and using them on data that clearly isn't (e.g. heavily skewed counts) gives misleading p-values.
Prerequisite
Builds directly on probability fundamentals — a distribution is just a rule assigning probabilities across all possible outcomes.