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

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 32E

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32. It may be shown that if Tn is any sequence of random variables such that TT and
if the variances of T and T exist, then lim infn Var(Tn) ≥ 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) → ∞.

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