12/7/20151 math 4030-2b conditional probability, independency, bayes theorem
TRANSCRIPT
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**Math 4030-2b
Conditional Probability, Independency, Bayes Theorem
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Conditional Probability (Sec. 3.6)If A and B are any events in S and P(B) 0, then the conditional probability of A given B is
P(A|B) **
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Conditional probabilityIf A and B are any events in S and P(B) 0, then the conditional probability of A given B is**
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Probability of Intersection(Product Rule)Using the conditional probability we can find P(AB) as
P(AB) = P(A|B)P(B), if P(B) 0 or P(AB) = P(B|A)P(A), if P(A) 0**
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Independent EventsIf P(A|B) = P(A) or P(B|A) = P(B), then A and B are called INDEPENDENT events.And hence:Two events A and B are independent if and only if P(AB) = P(A) P(B)**
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Rule of Total ProbabilityIf B1, B2, B3, , Bn are mutually exclusive events of which one must occur, then**
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Bayes Theorem (Sec. 3.7)**B1, B2, B3, , Bn are mutually exclusive events of which one must occur. A is a n event. Then for any r = 1, 2, , n
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