2. Show that the following statistics are invariant under location or scale or locationscale group:

(a) X−median(Xi).

(b) X(n+1−k)

−X(k).

(c)

n i=1

|Xi−X|/n.

(d)

ni

=1(Xi−X)(Yi−Y)

{ni

=1(Xi−X)2ni

=1(Yi−Y)2}1/2 , where (X1,Y1, . . . , (Xn,Yn) is a random sample from a bivariate distribution.