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Theorem 3-12. For n events A1, A2, An, we have 2,.... P(A10A20... nAn) = P(A,) P(A2\A1) P(A3\A¡ nA2) ... xP(A,I A1NA2...nAn 1) ... where P(A; I A¡n Ak n... n Aj) represents the conditional probability of the event A; given that the events Aj, Ak A, have already happened. ....

Theorem 3-12. For n events A1, A2, An, we have 2,.... P(A10A20... nAn) = P(A,) P(A2\A1) P(A3\A¡ nA2) ... xP(A,I A1NA2...nAn 1) ... where P(A; I A¡n Ak n... n Aj) represents the conditional probability of the event A; given that the events Aj, Ak A, have already happened. ....

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Prove the theorem

Theorem 3.12. For n events A1, A2, An, we have ••.. P(A1NA20... O An) = P (A¡) P(A2\A¡) P(A3\A1 n A2)... xP(A,I A¡ N An..n An -1) .. where P(A;| A¡n Ak n...n A) represents the conditional probability of the event A; given that the events A¡, Ak A¡ have already happened. ••..
Transcribed Image Text:Theorem 3.12. For n events A1, A2, An, we have ••.. P(A1NA20... O An) = P (A¡) P(A2\A¡) P(A3\A1 n A2)... xP(A,I A¡ N An..n An -1) .. where P(A;| A¡n Ak n...n A) represents the conditional probability of the event A; given that the events A¡, Ak A¡ have already happened. ••..
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