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.

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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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Question Posted: Nov 19, 2015 11:52 PM

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Develop a careful proof of Theoram 2.1 which states that for any events A and B, Pr

Question:

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)

Step by Step Answer:

First note that the sets A UB and B can be rewritten as AUBAUB B UB A...View the full answer

Probability and Random Processes With Applications to Signal Processing and Communications

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