Uniform Representation and Simulation of a Random Variable. For a distribution function F, its left-continuous inverse is Show that if U has a uniform distribution on the interval [0, 1], then the...

Uniform Representation and Simulation of a Random Variable. For a distribution function F, its left-continuous inverse is
Show that if U has a uniform distribution on the interval [0, 1], then the random variable X = F
⁻¹⁽U) has the distribution F. (Use the fact that F(x) ≥ u if and only if F
⁻¹(u) ≤ x.)