Lecture04-2010

# 3 given this construction the conditional probability

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Unformatted text preview: onditional event and marginal distribution functions are the same. 3. Given this construction the conditional probability can be derived as P [A|B ] = 2 AEB 6182 Agricultural Risk Analysis and Decision Making Professor Charles B. Moss Lecture IV Fall 2010 4. In our discussion of the role of the die P [x1 = 4, x2 = 6] = P [x1 = 4 and x2 = 6] 1/36 1 = = (6) P [x2 = 6] 1/6 6 D. Given that the events A1 , A2 , · · · An are mutually exclusive events such that P [A1 ∪ A2 ∪ · · · An ] = 1 the conditional probability can then be extended to Bayes Theorem P [ E | Ai ] P [ Ai ] P [ Ai | E ] = ￿ n P [E |Aj ] P [Aj ] (7) j =1 Given that P [A|B ] = P [A ∩ B ] ⇒ P [B ] P [A|B ] = P [A ∩ B ] P [B ] (8) Substituting this result into the previous expression P [Ai ∩ E ] P [ Ai | E ] = ￿ n P [Aj ∩ E ] (9) j =1 1. This expression uniﬁes the simple expression in Equation 5. Speciﬁcally, following the Axioms of Probability (Condition 3). P [A1 ] + P [A2 ] + · · · P [An ] = P [A1 ∪ A2 ∪ · · · An ] (10) 2. T...
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## This note was uploaded on 02/01/2012 for the course AEB 6182 taught by Professor Weldon during the Fall '08 term at University of Florida.

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