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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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6. Let {Xn, n € N} be a sequence of independent random variables exponentially distributed with param-
eter λ = 1. The law of large numbers (LLN) states that:
[A]P(2X. - 2 > €) → 0 for any e > 0 as n →∞.
[B]P(EX - }| > )
→ 0 for any € >0 as n → ∞.
[C] (Σ,(X-2)
(1-2)) → Z, in distribution as n → ∞o, where Z is a standard normal.
√4n
[D] (²²–1(X₁-³)) → Z, in distribution as n → ∞, where Z is a standard normal.

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