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# PS RAO 2 - Chapter 2 Axioms of Probability Let S denote a...

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Chapter # 2 Axioms of Probability: Let S denote a sample space for an expe- riment, then P[S]=1 P[A] 0 for every event A •Let A 1 ,A 2 ,A 3 ,… be a finite or an infinite collection of mutually exclusive events, then P[A 1 A 2 A 3 ….]=P[A 1 ]+P[A 2 ]+p[A 3 ]+…. .

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The first two axioms are obvious, since one defines a certain event and the other non- negativity. The third axioms defines about mutually exclu sive events when the sample points in the sample space for the experiment are not equally likely. The consequence of these axioms results the following property: P[ ]=0
Proof: for any event A, we can write A=A , since A and are mutually exclusive , it follows by 3 rd axiom, P[A]=P[A ]=P[A]+P[ ] P[ ]=0 Another consequence of these axioms is that P[A 1 ]= 1-P[A] Proof:If A is an event in S we can write S=A A 1 , using the axioms 2 and 3,

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P[S]=P[A]+P[A 1 ] P[A]=1-P[A 1 ] General addition rule : If A 1 and A 2 are any two events, then
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PS RAO 2 - Chapter 2 Axioms of Probability Let S denote a...

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