Develop a careful proof of Theoram 2.1 which states that for any events A and B, Pr
Question:
Develop a careful proof of Theoram 2.1 which states that for any events A and B,
Pr (A U B) = Pr (A) + Pr (B) – Pr (A ∩ B).
One way to approach this proof is to start by showing that the set can be written as the union of three mutually exclusive sets,
And hence by Corollary 2.1,
Next, Show that
And likewise
Put these results together to complete the desired proof.
Transcribed Image Text:
Pr. (A U B) = Pr (A n (ATB)) + Pr (A n B) + Pr (B n (A nB)) Pr (A n {A n B)) = Pr (A)-Pr (A n B) Pr (B n {A n B) = Pr (B)-Pr (A n B)
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First note that the sets A UB and B can be rewritten as AUBAUB B UB A...View the full answer
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Related Book For
Probability and Random Processes With Applications to Signal Processing and Communications
ISBN: 978-0123869814
2nd edition
Authors: Scott Miller, Donald Childers
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