Use Ferguson’s Theorem 3 (A course in Large Sample Theory)to show that if Xn converges in distribution to X, then for any ε > 0, there exists a number B and some integer N such that if n ≥ N, then Pr[|Xn| ≥ B] < ε.
Use Ferguson’s Theorem 3 (A course in Large Sample Theory)to show that if Xn converges in distribution to X, then for any ε > 0, there exists a number B and some integer N such that if n ≥ N, then Pr[|Xn| ≥ B] < ε. The property you are showing here is ”tightness”. Hint: […]