Exercise 44 (#7.85, #7.86). Let (X1, .... X,) be a random sample from a continuous cumulative distribution function F on R that is twice differentiable at 0 = F-1). 0 0. (i) Let {hin} be a sequence of integers satisfying hi=pten-1/2 +0(n-1/2) with a constant c. Show that Vn( X (km) ) = c/F'() + 0(1) a.s., where yo) is the jth order statistic and is the sample pth quantile. (ii) Show that vn ( him) 6)F"() + N(C,p(1 p)). (iii) Let {hin} and {k2n} be two sequences of integers satisfying 1