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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 [AB ] =
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 [AB ] = P [A ∩ B ]
⇒ P [B ] P [AB ] = 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.
 Fall '08
 Weldon

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