Inverse Transform Sampling

Definition

$X=F_X^{-1}(U)$

we can generate $X$ with CDF $F_X(x)$ by using inverse function of CDF $F_X^{-1}$ and uniform random variable $U\sim u[0,1]$

Facts

Let $U\sim u(0,1)$ and $F$ be continuous CDF, then $F^{-1}(U)\sim F$