3.5 Let X1, . . . ,Xn be independent observations with distribution function F(x − ), and let Tn = Pn i=1 cniXn:i be an L-estimator of , then:

(a) If Pn i=1 cni = 1, then T is translation equivariant.

(b) If F is symmetric about zero, Pn i=1 cni = 1 and cni = cn,n−i+1, i =

1, . . . , n, then the distribution of Tn is symmetric about .