1. Show that the following statistics are equivariant under translation group:

(a) Median (Xi).

(b) (X(1)+X(n))/2.

(c) X[np]+1, the quantile of order p, 0 < p < 1.
(d)
X(r)+X(r+1)+· · ·+X(n−r)
/(n−2r).

(e) X+Y, where Y is the mean of a sample of size m, m = n.