Explanation The indicator function is given as follows: I A ( x ) = { 1 if x ∈ A 0 if x ∉ A The indicator functions for B , A ∩ B , and A ∪ B are as follows: I B ( x ) = { 1 if x ∈ B 0 if x ∉ B I A ∩ B ( x ) = { 1 if x ∈ A ∩ B 0 if x ∉ A ∩ B I A ∪ B ( x ) = { 1 if x ∈ A ∪ B 0 if x ∉ A ∪ B The function I A ( x ) ⋅ I B ( x ) is determined as follows: I A ( x ) I B ( x ) = { 1 if x ∈ A 0 if x ∉ A ⋅ { 1 if x ∈ B 0 if x ∉ B = { 1 ⋅ 1 if x ∈ A and x ∈ B 1 ⋅ 0 if x ∈ A and x ∉ B 0 ⋅ 1 if x ∉ A and x ∈ B 0 ⋅ 0 if x ∉ A and x ∉ B = { 1 if x ∈ A and x ∈ B 0 if x ∈ A and x ∉ B 0 if x ∉ A and x ∈ B 0 if x ∉ A and x ∉ B = { 1 if x ∈ A ∩ B 0 if x ∉ A ∩ B = 1 A ∩ B The function min ( I A I B ) is determined as follows: min ( I A I B ) = min ( { 1 if x ∈ A 0 if x ∉ A ⋅ { 1 if x ∈ B 0

Mathematical Statistics and Data Analysis

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ISBN: 9781111793715

Author: John A. Rice

Publisher: Cengage Learning

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Chapter 2.5, Problem 6P

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Verify that IA∩B=IAIB=min(IA,IB) and IA∪B=max(IA,IB).

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Chapter 2 Solutions

Mathematical Statistics and Data Analysis

Ch. 2.5 - Prob. 1P Ch. 2.5 - Prob. 2P Ch. 2.5 - Prob. 3P Ch. 2.5 - Prob. 4P Ch. 2.5 - Prob. 5P Ch. 2.5 - Prob. 6P Ch. 2.5 - Prob. 7P Ch. 2.5 - Prob. 8P Ch. 2.5 - Prob. 9P Ch. 2.5 - Prob. 10P

Ch. 2.5 - Prob. 11P Ch. 2.5 - Prob. 12P Ch. 2.5 - Prob. 13P Ch. 2.5 - Prob. 14P Ch. 2.5 - Prob. 15P Ch. 2.5 - Prob. 17P Ch. 2.5 - Prob. 18P Ch. 2.5 - Prob. 19P Ch. 2.5 - Prob. 20P Ch. 2.5 - Prob. 21P Ch. 2.5 - Prob. 22P Ch. 2.5 - Prob. 23P Ch. 2.5 - Prob. 24P Ch. 2.5 - Prob. 25P Ch. 2.5 - Prob. 26P Ch. 2.5 - Prob. 27P Ch. 2.5 - Prob. 28P Ch. 2.5 - Prob. 29P Ch. 2.5 - Prob. 30P Ch. 2.5 - Prob. 31P Ch. 2.5 - Prob. 32P Ch. 2.5 - Prob. 33P Ch. 2.5 - Prob. 34P Ch. 2.5 - Prob. 35P Ch. 2.5 - Prob. 36P Ch. 2.5 - Prob. 37P Ch. 2.5 - Prob. 38P Ch. 2.5 - Prob. 39P Ch. 2.5 - Prob. 40P Ch. 2.5 - Prob. 41P Ch. 2.5 - Prob. 42P Ch. 2.5 - Prob. 43P Ch. 2.5 - Prob. 44P Ch. 2.5 - Prob. 45P Ch. 2.5 - Prob. 46P Ch. 2.5 - Prob. 47P Ch. 2.5 - Prob. 48P Ch. 2.5 - Prob. 49P Ch. 2.5 - Prob. 50P Ch. 2.5 - Prob. 51P Ch. 2.5 - Prob. 52P Ch. 2.5 - Prob. 53P Ch. 2.5 - Prob. 54P Ch. 2.5 - Prob. 55P Ch. 2.5 - Prob. 56P Ch. 2.5 - Prob. 57P Ch. 2.5 - Prob. 58P Ch. 2.5 - Prob. 59P Ch. 2.5 - Prob. 60P Ch. 2.5 - Prob. 61P Ch. 2.5 - Prob. 62P Ch. 2.5 - Prob. 63P Ch. 2.5 - Prob. 64P Ch. 2.5 - Prob. 65P Ch. 2.5 - Prob. 66P Ch. 2.5 - Prob. 67P Ch. 2.5 - Prob. 68P Ch. 2.5 - Prob. 69P Ch. 2.5 - Prob. 70P

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Verify that I A ∩ B = I A I B = min ( I A , I B ) and I A ∪ B = max ( I A , I B ) .

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Verify that IA∩B=IAIB=min(IA,IB) and IA∪B=max(IA,IB).

Chapter 2 Solutions