continuous uniform distribution

A continuous uniform random variable is a continuous random variable with a constant probability density function on a given interval and a value of zero elsewhere. Such a random variable has a continuous uniform distribution, denoted $X\sim \mathrm{Unif}(a,b)$, where $a,b$ are the endpoints of the interval.

Formally,
if $X$ is a continuous uniform random variable, i.e. $X\sim \mathrm{Unif}(a,b)$, then its probability density function is

N.B. when $X$ is a continuous random variable, $P(X=x)=0$ for any particular $x$; therefore, the probabilities of open and closed intervals are identical.