2.34 Let Sn(x) be the empirical distribution function for a random sample of size n from the uniform (0, 1) distribution. Define Xn(t) ¼

ffiffiffi np jSn(t)  tj Zn(t) ¼ (t þ 1)Xn[t=(t þ 1)] for all 0  t  1 Find E[Xn(t)], E[Zn(t)], var[Xn(t)] and var[Zn(t)], and conclude that var[Xn(t)]  var[Zn(t)] for all 0  t  1 and all n.