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.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.1: Continuous Probability Models
Problem 32E
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