Let [math]X[/math] be a random variable with cumulative distribution function [math]F[/math] strictly increasing on the range of [math]X[/math]. Let [math]Y = F(X)[/math]. Show that [math]Y[/math] is uniformly distributed in the interval [math][0,1][/math]. (The formula [math]X = F^{-1}(Y)[/math] then tells us how to construct [math]X[/math] from a uniform random variable [math]Y[/math].)