The continuous uniform distribution is the simplest continuous probability model: every value in an interval [a, b] is equally likely, so the probability density function is a flat, rectangular curve of constant height 1/(b-a). Because the density is constant, probabilities become areas of rectangles, which means you can often compute them with basic geometry instead of calculus. This makes the uniform distribution an ideal starting point for Module 5, where you move from discrete random variables and probability mass functions to continuous random variables described by a PDF and a cumulative distribution function (CDF).
In engineering practice, the uniform distribution models situations where you know only the range of possible values and have no reason to favor one value over another: waiting time for a bus that arrives every 10 minutes, rounding or measurement error within a tolerance band, or random number generation in simulation studies. It is also the building block for Monte Carlo methods, where uniform random numbers are transformed into samples from other distributions. Knowing its mean (a+b)/2 and variance (b-a)^2/12 lets you summarize such scenarios quickly.
As you watch the videos below, pay attention to three things: how the height of the density is determined from the endpoints a and b, how a probability statement such as P(X < c) or P(c < X < d) is translated into an area or into the CDF expression (x-a)/(b-a), and how conditional or "given that" problems shrink the interval you are working with. Try pausing each worked example, solving it yourself, and then comparing your setup to the one on screen.
A compact overview of the continuous uniform distribution that defines the distribution, introduces its parameters a and b, and shows the rectangular shape of the density function. The video then works through example probability problems of the type you will see on homework and exams. Expect the key formulas for probabilities, and likely the mean and standard deviation, to be stated and applied.
At about six minutes it is an efficient first pass that covers the "what is it," "parameters," and "calculating probabilities" subtopics in one place, with a worked-example style that matches the problem-solving focus of this course.
A focused example video built around a dish-washing time scenario, in which a quantity is assumed to be uniformly distributed over a fixed interval. As the description notes, it demonstrates two different ways to arrive at the same probability, which typically means computing the area under the flat density geometrically and then using the cumulative distribution function.
Seeing the same answer obtained two ways reinforces the link between the PDF (area) and the CDF (accumulated probability), and Mathispower4u is a reliable, carefully worked source for step-by-step statistics examples.
A longer, more mathematical treatment that derives the properties of the uniform distribution, including the mean, the variance, and the moment generating function. The derivations use integration of the density function rather than just quoting formulas, giving you the reasoning behind (a+b)/2 and (b-a)^2/12.
This fills in the theory behind the shortcut formulas used in the other two videos, which is useful if you want to understand why the results hold; note that the MGF material goes beyond what this course requires, so treat it as optional enrichment.
Together these videos build from definition to derivation. The first and second support MO1 by showing how a continuous random variable is described by a flat PDF and an accumulating CDF, in contrast to discrete probability mass functions, and they directly serve MO2 by demonstrating how to compute P(X < c) and P(c < X < d) using both area and cumulative-function approaches. The applied scenarios, such as timing and waiting-time examples, give practice with MO3 and MO4: recognizing when "equally likely across a range" is a reasonable modeling assumption, and stating what a computed probability means for a decision. The third video deepens your grasp of the mean and variance formulas so that you can summarize and interpret uniform models rather than only plugging into them.
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.