Suppose we know a random variable [math]Y[/math] as a function of the uniform random variable [math]U[/math]: [math]Y = \phi(U)[/math], and suppose we have calculated the cumulative distribution function [math]F_Y(y)[/math] and thence the density [math]f_Y(y)[/math]. How can we check whether our answer is correct? An easy simulation provides the answer: Make a bar graph of [math]Y = \phi(\mbox{$rnd$})[/math] and compare the result with the graph of [math]f_Y(y)[/math]. These graphs should look similar. Check your answers to Exercise and Exercise by this method.