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A uniform distribution, also called a rectangular distribution, is a probability distribution that has constant probability. This distribution is defined by two parameters , a and b: a is the minimum.
All values in the distribution have a constant probability, making them uniformly distributed. This distribution is also known as the rectangular distribution because of its shape in probability distribution plots, as I’ll show you below. Uniform distributions come in both discrete and continuous varieties of probability distributions.
A uniform distribution is a type of symmetric probability distribution in which all the outcomes have an equal likelihood of occurrence. There are two types of uniform distributions: discrete and continuous.
Sometimes, we also say that it has a rectangular distribution or that it is a rectangular random variable. To better understand the uniform distribution, you can have a look at its density plots. Expected value. The expected value of a uniform random variable is. Proof. Variance. The variance of a uniform random variable is. Proof.
2 kwi 2023 · Figure \(\PageIndex{1}\) This graph shows a uniform distribution. The horizontal axis ranges from 0 to 15. The distribution is modeled by a rectangle extending from x = 0 to x = 15. A region from x = 2 to x = 18 is shaded inside the rectangle.
Rectangular (a.k.a. Uniform) Distribution The Rectangular Distribution is a function that represents a continuous uniform distribution and constant probability. In a rectangular distribution, all outcomes are equally likely to occur. The rectangular distribution is the most commonly used probability distribution in uncertainty analysis.
Example 1. Using the continuous uniform distribution function. For a random variable find. In a graphical representation of the continuous uniform distribution function the area under the curve within the specified bounds, displaying the probability, is a rectangle.
