Uniformly distributed : A random variable $X$ is uniformly distributed on the interval $[a,b]$ if it only takes values in $[a,b]$ and any value within the interval is equally likely in the sense of $P[X\lt x]=\frac{x-a}{b-a}.$ for $a\leq x\leq b.$ A uniformly distributed random variable has a mean $E[X]=\frac{a+b}{2}$ and a variance of $var[X]=\frac{(b-a)^2}{12}.$