need help

In class you were told that that the null distribution of the Wilcoxon test is only valid when F(x)=G(x) and that even when F and G were symmetric distributions with the same mean but their variances differ the true variance of the Wilcoxon statistic now differs from the formula: (m+n+1)/(12mn). Give an example demonstrating the correctness of the above claim. Hint: Choose a distribution that is easy to work with, Le. calculate the variance of W under the alternative. Use R to perform a small simulation verifying your result (include your program in the answer)