Example 3 Suppose we want to apply the Rejection method to simulate the random variable with

       We can choose and so that

                                  

       We can now apply the rejection method to simulate .

    Testing the closeness of the random data to a theoretical distribution

       Once we have the generated random data, we have to test how closely they fit the theoretical distribution. We can do so by comparing the frequencies observed in the random data to the expected frequencies of the theoretical distribution.