Let m=n=1 and X1 F, Y1 G, where F and G are Bernoulli with success probability p and q.

1. What is the unconditional distribution of the Wilcoxon stat under null hypothesis F= G (ie. p = q)

2. Does the null distribution depend on p and what is the consequence of this finding for practical applications of the Wilcoxon when F and G aren't continuous?

3. Is the null distribution from 1. the same as the one used when adjusting for ties? Give a brief explanation.