Definition:Uniform Distribution/Continuous

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Let $X$ be a continuous random variable on a probability space $\struct {\Omega, \Sigma, \Pr}$.

Let $a, b \in \R$ such that $a < b$.

$X$ is said to be uniformly distributed on the closed real interval $\closedint a b$ if and only if it has probability density function:

$\map {f_X} x = \begin{cases} \dfrac 1 {b - a} & a \le x \le b \\ 0 & \text{otherwise} \end{cases}$

This is written:

$X \sim \ContinuousUniform a b$

Also see

  • Results about the continuous uniform distribution can be found here.

Technical Note

The $\LaTeX$ code for \(\ContinuousUniform {a} {b}\) is \ContinuousUniform {a} {b} .

When the arguments are single characters, it is usual to omit the braces:

\ContinuousUniform a b