Lecture04-2010

# Given that a1 a2 an are exhaustive or a1 a2 an

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: hus, the denominator of Equation 7 becomes P [A1 ∩ E ]+P [A2 ∩ E ]+· · · P [An ∩ E ] = P [(A1 ∪ A2 ∪ · · · An ) ∩ E ] (11) 3. Given that A1 , A2 , · · · An are exhaustive, or A1 ∪ A2 ∪ · · · An = C the entire sample space since P [A1 ∪ A2 ∪ · · · An ] = 1 P [(A1 ∪ A2 ∪ · · · An ) ∩ E ] = P [C ∪ E ] = P [E ] with the last equality since E ⊂ C . 3 (12) AEB 6182 Agricultural Risk Analysis and Decision Making Professor Charles B. Moss Lecture IV Fall 2010 4. Returning to the numerator in Equation 7 P [E ] = n ￿ i=1 P [E |Ai ] P [Ai ] (13) 5. Deﬁnition 2.11 p-20 Two events A and B are independent if P [A] = P [A|B ]. a. In die example P [x1 = 4] = P [x1 = 4|x2 = 6] = 1 6 (14) II. Some Useful Distributrion Functions A. Univariate normal distribution ￿ f x|µ, σ 2 ￿ ￿ 1 ( x − µ) 2 = √ exp − 2σ 2 σ 2π ￿ (15) B. Multivariate normal distribution ￿ 1 1 f (x|µ, Σ) = √ |Σ|−1/2 exp − (x − µ)￿ Σ−1 (x − µ) 2 2π σ11 σ12 · · · σ1n σ21 σ22 · · · σ2n σij Σ= . . .. . ρij √ . . σii σjj . . . . . σn1...
View Full Document

## 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.

Ask a homework question - tutors are online