So far this module you have met the discrete distributions one at a time: the Bernoulli and binomial, the geometric and negative binomial, the hypergeometric, and the Poisson. Real problems do not arrive labeled. This topic is about the step that comes first in practice — reading a scenario carefully, deciding which model its assumptions actually match, and then setting up the parameters (n and p, or lambda and the time or space interval) before touching a formula.
Once the model is chosen, the rest of the work is mechanical but easy to get wrong: translating phrases like "at least three," "no more than two," or "the first success" into the correct sum of probability mass function terms, deciding when a complement is faster, and then computing the expected value and variance so you can say something about the long-run behavior of the process, not just a single event. The final step — interpreting the number in context — is what makes the analysis useful to an engineer or a decision maker.
The three videos below are worked-problem and conceptual supports. As you watch the two binomial examples, pay attention to how the speaker identifies n, p and x from the wording of the problem, and how cumulative and "at least" questions are organized. In the third video, focus on the reasoning that links counts of events in an interval to the waiting time between events — that connection is a common source of confusion when you are deciding whether a scenario is Poisson at all.
A worked example in which an unemployment-rate scenario for a county is modeled as a binomial experiment and several probabilities are computed to four decimal places. Based on the title and description, expect the instructor to identify the number of trials and the success probability from the problem statement and then evaluate exact and cumulative binomial probabilities.
It models the exact workflow of this topic — confirm the distribution, extract parameters, compute, round and report — using a social and economic data setting that shows these tools are not limited to manufacturing examples.
A second binomial worked problem, this time built around a fast-food promotional game where each game piece is a trial with a fixed win probability. The video should walk through setting up n and p and calculating probabilities, again carried to at least four decimal places.
Having a second, differently framed binomial example helps you see which features of a scenario actually signal "binomial" (fixed trials, two outcomes, constant probability, independence) rather than memorizing one problem type.
Steve Brunton explains how the exponential distribution describes the waiting time until the next event in a Poisson process, connecting the count-based view of random events to the time-between-events view. Expect conceptual derivation and intuition rather than a numerical homework problem.
It strengthens your judgment about when a scenario really satisfies Poisson conditions, and the clear, well-regarded engineering presentation helps you interpret lambda correctly as a rate per unit interval.
The two binomial examples directly support MO4 by demonstrating parameter identification and exact probability computation for applied scenarios, and they reinforce MO1 and MO2 by showing how the probability mass function assigns probabilities across all outcomes and how those probabilities summarize long-run behavior. The Poisson-exponential video supports MO3 by clarifying the defining conditions of a Poisson process, which is the key test you apply when deciding between binomial and Poisson models. Across all three, the emphasis on explaining what the resulting numbers mean for the unemployment, promotional-game or event-timing context supports MO5, and the expected value and variance discussion in context connects back to MO2.
These videos were chosen from YouTube on October 2, 2026. Each has captions; the player turns them on. Videos on YouTube can be changed or removed — if one no longer plays, tell your instructor. If a player does not appear, use its Watch on YouTube link.