This exercise is related to some of the details in Example 14.9. (i) Show that n =

This exercise is related to some of the details in Example 14.9.

(i) Show that ξn = n{θ − X(n)}/θ converges weakly to Exponential(1).

(ii) Show that for any k ≥ 1,

(iii) Show that (14.45) and (14.55) imply lim supΔn = ∞ a.s. and lim inf δn = 0 a.s.

Transcribed Image Text:

P{X) Xn-k+1)|X1,..., Xn) x-(1-2)" 1 = (1 - 4)". n