4. (a) Non-parametric statistics tries to make minimal assumption on the underlying dis- tributions. Let X ~ F. Do we need to make any assumptions (e.g. normality) on F to study the distribution of F(X)? If yes, state the assumption(s) and result. If no, state the reason. (b) For a sample of n observations {X1, ..., X,}, let {R1, ..., Rn} be its rank statistics and Fr(x) be its empirical distribution function. Show that Fr (X.)= n for i = 1, ..., n. (You may assume that there is no tie.) (c) In view of (a) and (b), comment on the advantage(s) of using the ranks as a statistical tool