9. Let (,S,P) be a probability space. Let A, B, C S with PB and PC

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9. Let (Ω,S,P) be a probability space. Let A, B, C ∈ S with PB and PC > 0. If B and C are independent show that P{A | B} = P{A | B∩C}PC+P{A | B∩Cc}PCc.

Conversely, if this relation holds, P{A | BC} = P{A | B}, and PA > 0, then B and C are independent (Strait [111]).

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An Introduction To Probability And Statistics

ISBN: 9781118799642

3rd Edition

Authors: Vijay K. Rohatgi, A. K. Md. Ehsanes Saleh

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Question Posted: Sep 07, 2024 12:01 PM

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9. Let (,S,P) be a probability space. Let A, B, C S with PB and PC

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An Introduction To Probability And Statistics

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