The Poisson distribution models the number of times an event occurs within a fixed interval of time, length, area, or volume — the number of defects per meter of weld, calls arriving at a help desk per hour, or particles detected per second. Instead of a fixed number of trials like the binomial distribution, the Poisson distribution is built around a single rate parameter, lambda, which represents the average number of occurrences per interval.
In this course the Poisson distribution matters for two reasons. First, it is the natural model whenever you are counting rare events over a continuum, which describes a large share of reliability, quality control, and queueing problems in engineering. Second, it has an unusually clean structure: the probability mass function depends on a single parameter, and both the mean and the variance equal lambda. That makes it a good distribution for practicing the general skills of this module — verifying that probabilities sum to one, computing expected value and variance, and interpreting those numbers in context.
As you watch, pay attention to three things: how lambda is identified and rescaled when the interval in the problem differs from the interval in which the rate was reported; the exact form of the probability formula and how factorials and the exponential term are evaluated; and the conditions (independence, constant average rate, events occurring one at a time) that justify using Poisson rather than binomial. Keep a running list of worked examples so you can recognize problem types on an exam.
A concise, engineering-oriented introduction to the Poisson distribution from LearnChemE, a video series produced by faculty in the Department of Chemical and Biological Engineering at the University of Colorado Boulder. In about ten minutes it should present the Poisson probability formula, explain the role of the rate parameter, and work through example calculations of the type found in engineering statistics textbooks.
It is the shortest and most course-aligned of the three videos, produced by engineering faculty and organized around standard textbooks, so it fits the applied framing of this module and is a good first watch.
A longer, lecture-style treatment of the Poisson distribution covering what it is, how the probability formula is written, and how to apply it to problems. Expect a steady walk through the derivation or motivation of the formula followed by multiple solved examples. The video offers both Hindi and English audio tracks, selectable through the settings icon.
The extended runtime allows more worked problems than a short overview, which directly supports the subtopics on the probability formula and applying Poisson to real-world problems.
A companion video focused specifically on the mean and variance of the Poisson distribution. It should show how both quantities are obtained from the probability mass function and establish the distinctive result that the mean and variance are both equal to lambda. Like the other video from this channel, it is available with English audio.
It targets the mean-and-variance subtopic directly, giving you the derivation behind a result that is easy to memorize but important to understand and to contrast with the binomial case.
Together these videos move from the structure of the Poisson probability mass function to its parameters and applications. The formula-focused segments support MO4 by showing how to identify lambda correctly for a given interval and compute exact probabilities, and they reinforce MO1 by demonstrating that Poisson probabilities are non-negative and sum to one across all non-negative integer counts. The mean-and-variance video addresses MO2 and gives you the key fact that both equal lambda. The discussion of when Poisson applies — independent events at a constant average rate over a continuum, with no fixed number of trials — equips you to meet MO3 by distinguishing Poisson from binomial scenarios, and the worked engineering and real-world examples across all three videos model the contextual interpretation required by MO5.
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.