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) → ∞.
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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) → ∞.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F66f52ea3-13fd-4902-bc86-2f48a4cfbf0d%2F5d7cb6ba-54f5-45d0-abc9-586c8d0200e9%2F2qg6sbv_processed.png&w=3840&q=75)
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