uniform (continuous) random variable

A random variable $X$ is said to be a () random variable with parameters $a$ and $b$ if its probability density function is given by

$f_X(x)={\displaystyle \frac{1}{b-a}},x\in [a,b],$

and is denoted $X\sim U(a,b)$.

Notes:

1. They are also called rectangular distributions, considers that all points in the interval $[a,b]$ have the same mass.

2. $E[X]=\frac{a+b}{2}$

3. $Var[X]=\frac{{(b-a)}^2}{12}$

4. $M_X(t)=\frac{e^{bt}-e^{at}}{(b-a)t}$