=+a Show that SmYi;i 1; 2; ... ; n, is uniformly distributed over the set of points 0; 1=m; 2=m; ... ; 1. b

=+ðaÞ Show that SmðYiÞ;i ¼ 1; 2; ... ; n, is uniformly distributed over the set of points ð0; 1=m; 2=m; ... ; 1Þ.

ðbÞ Show that the distribution of SmðYðjÞÞ  SmðYðkÞÞ; k < j, is the same as the distribution of SmðYðjkÞÞ. (Fligner and Wolfe, 1976)

ðcÞ Show that the distribution of PðiÞ ¼ mSmðYðiÞÞ is given by P½PðiÞ ¼ j ¼

m þ n  i  j m  j i þ j  1 j

m þ n n j ¼ 0; 1; ... ; m