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23. Suppose {An} are events. (a) If for each k show (d) Show iff 8 n-l EP(An (A) = 00, n=k i=k (b) What is the relevance to the Borel Zero-One Law? (c) Is it enough to assume P(lim sup An) = 1. 88 8 n=1 n-1 PO P(A₁4₁) = ∞o? i=1 P (lim sup An) = 1 81x 8 Σ P(AAn) = 00 n=1 for all events A such that P(A) > 0.

23. Suppose {An} are events. (a) If for each k show (d) Show iff 8 n-l EP(An (A) = 00, n=k i=k (b) What is the relevance to the Borel Zero-One Law? (c) Is it enough to assume P(lim sup An) = 1. 88 8 n=1 n-1 PO P(A₁4₁) = ∞o? i=1 P (lim sup An) = 1 81x 8 Σ P(AAn) = 00 n=1 for all events A such that P(A) > 0.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 54E
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23. Suppose (An) are events. (a) If for each k show (d) Show iff 8 n=k (b) What is the relevance to the Borel Zero-One Law? (c) Is it enough to assume n-l P(A₂A) = ∞, i=k P (lim sup An) = 1. 848 n=1 n-1 P(A₂A) = ∞o? i=1 P P (lim sup An) = 1 818 8 ΣP(AA,) = ∞o n=1 for all events A such that P(A) > 0.
Transcribed Image Text:23. Suppose (An) are events. (a) If for each k show (d) Show iff 8 n=k (b) What is the relevance to the Borel Zero-One Law? (c) Is it enough to assume n-l P(A₂A) = ∞, i=k P (lim sup An) = 1. 848 n=1 n-1 P(A₂A) = ∞o? i=1 P P (lim sup An) = 1 818 8 ΣP(AA,) = ∞o n=1 for all events A such that P(A) > 0.
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