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1. For a sequence of events A,, n ≥ 1, we write A, † A if A₁ CA₂ C ... and A = U₁A₁. Similarly we write A↓ A if A₁1 A₂ ... and A=nAn. Show that i) if A ↑ A then lim P(An) = P(A).

1. For a sequence of events A,, n ≥ 1, we write A, † A if A₁ CA₂ C ... and A = U₁A₁. Similarly we write A↓ A if A₁1 A₂ ... and A=nAn. Show that i) if A ↑ A then lim P(An) = P(A).

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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1. For a sequence of events A₁, n ≥ 1, we write A ↑ A if A₁ CA₂ C ... and A = U₁A. Similarly we write An A if A₁ A₂... and A=4₂. Show that i) if An ↑ A then limn- P(An) = P(A). ii) if An A then lim P(A) = P(A). 2-0
Transcribed Image Text:1. For a sequence of events A₁, n ≥ 1, we write A ↑ A if A₁ CA₂ C ... and A = U₁A. Similarly we write An A if A₁ A₂... and A=4₂. Show that i) if An ↑ A then limn- P(An) = P(A). ii) if An A then lim P(A) = P(A). 2-0
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