Continuous uniform distribution
Standard uniform distribution

The continuous uniform distribution with parameters a = 0 {\displaystyle a=0} and b = 1, {\displaystyle b=1,} i.e. U (0, 1), {\displaystyle U(0,1),} is called the standard uniform distribution.

One interesting property of the standard uniform distribution is that if u 1 {\displaystyle u_{1}} has a standard uniform distribution, then so does 1 − u 1. {\displaystyle 1-u_{1}.} This property can be used for generating antithetic variates, among other things. In other words, this property is known as the inversion method where the continuous standard uniform distribution can be used to generate random numbers for any other continuous distribution. If u 1 {\displaystyle u_{1}} is a uniform random number with standard uniform distribution, i.e. with U (0, 1), {\displaystyle U(0,1),} then x = F − 1 (u 1) {\displaystyle x=F^{-1}(u_{1})} generates a random number x {\displaystyle x} from any continuous distribution with the specified cumulative distribution function F. {\displaystyle F.}
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