Problem 3 Let = N and A = P(N). Let P: A → [0, 1] be a function with the property that for all A, B E A P(A) = P(B) Show that P does not qualify as a probability measure. Hint: Try a proof by contradiction. To this end, assume that P is a probability measure. Define the sets An = {1,...,n} and use the continuity from below and the additivity of the prob- ability measures to show that the initial assumption leads to a contradiction. #A = #B.
Problem 3 Let = N and A = P(N). Let P: A → [0, 1] be a function with the property that for all A, B E A P(A) = P(B) Show that P does not qualify as a probability measure. Hint: Try a proof by contradiction. To this end, assume that P is a probability measure. Define the sets An = {1,...,n} and use the continuity from below and the additivity of the prob- ability measures to show that the initial assumption leads to a contradiction. #A = #B.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![Problem 3
property that for all A, B E A
Let = N and A = P(N). Let P: A
-
[0, 1] be a function with the
P(A) = P(B)
Show that P does not qualify as a probability measure.
Hint: Try a proof by contradiction. To this end, assume that P is a probability measure.
Define the sets An = {1,...,n} and use the continuity from below and the additivity of the prob-
ability measures to show that the initial assumption leads to a contradiction.
#A = #B.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4575c695-56bc-4a6a-843f-ec886ca258f2%2F94ed534f-dcab-4599-9e09-725ce3f88229%2F9pz4zew_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 3
property that for all A, B E A
Let = N and A = P(N). Let P: A
-
[0, 1] be a function with the
P(A) = P(B)
Show that P does not qualify as a probability measure.
Hint: Try a proof by contradiction. To this end, assume that P is a probability measure.
Define the sets An = {1,...,n} and use the continuity from below and the additivity of the prob-
ability measures to show that the initial assumption leads to a contradiction.
#A = #B.
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Given : Let, and be a function with
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