A uniform distribution is a type of probability distribution where all outcomes are equally likely within a specified range. It is defined by two parameters: the minimum value (a) and the maximum value (b). The probability density function (PDF) for a continuous uniform distribution is constant across the interval ([a][b]), while the cumulative distribution function (CDF) describes the probability that a random variable will take a value less than or equal to a specific value.

For a continuous uniform distribution, the PDF is given by (f(x) = \frac{1}{b-a}) for (a \leq x \leq b), and the CDF is (F(x) = \frac{x-a}{b-a}) for (a \leq x \leq b). The mean of the distribution is (\mu = \frac{a + b}{2}) and the variance is (\sigma^2 = \frac{(b - a)^2}{12}) ²³.

In programming, such as in R or Python, functions are available to calculate the PDF and CDF for uniform distributions, making it easier to work with these distributions in data analysis and simulations ⁴⁵.