32. It may be shown that if Tn is any sequence of random variables such that TT andif the variances of T and T exist, then lim infn Var(Tn) ≥ Var(T). LetTn = X1[|X| ≤ 1 − n¯¹] +n1[|X| > 1 − n¯¹]where X is uniform, U(−1,1). Show that as n → ∞, Tn ✩ X, but Var(T) → ∞.

We are given that if Tn→LT and the variances of T and Tn exist, then:lim…

Answered: 32. It may be shown that if Tn is any…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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32. It may be shown that if Tn is any sequence of random variables such that TnT and if the variances of T and Tn exist, then lim inf, Var(T) ≥ Var(T). Let Tn = X1[|X| ≤ 1 − n¯¹] + n1[|X| > 1 − n¯¹] where X is uniform, U(-1, 1). Show that as n → ∞, Tn ✩ X, but Var(T) → ∞.