32. Prove Theorem 12 by making use of the following generalization of the distributive law: An (B₁UB₂ U U B₂) = (An B₂) u (An B₂) U... U (An B₂) THEOREM 12. If the events B₁, B2,...., and Be constitute a partition of the sample space S and P (B.) #0 for i= 1,2, ..., k, then for any event A in S P(A)=P(B.) P(A|B.).
32. Prove Theorem 12 by making use of the following generalization of the distributive law: An (B₁UB₂ U U B₂) = (An B₂) u (An B₂) U... U (An B₂) THEOREM 12. If the events B₁, B2,...., and Be constitute a partition of the sample space S and P (B.) #0 for i= 1,2, ..., k, then for any event A in S P(A)=P(B.) P(A|B.).
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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
Transcribed Image Text:32. Prove Theorem 12 by making use of the following generalization of the distributive law:
An (B₁UB₂UUB) = (An B₁) U (An B₂) UU(An B₂)
THEOREM 12. If the events B₁, B2,..., and B constitute a partition of the sample space S and
P (B₁) 0 for i= 1,2, ...,k, then for any event A in S
P(A)=P(B.) P(A | B₁).
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