Continuous Uniform Distribution
|Probability density function
Using maximum convention
|Cumulative distribution function
|Mode||any value in|
The (continuous) uniform distribution, as its name suggests, is a distribution with probability densities that are the same at each point in an interval. In casual terms, the uniform distribution shapes like a rectangle.
Mathematically speaking, the probability density function of the uniform distribution is defined as
And the cumulative distribution function is:
We derive the mean as follows.
As the uniform distribution is 0 everywhere but [a, b] we can restrict ourselves that interval
We use the following formula for the variance.