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Unformatted text preview: is P(D1=1  sum is 4)? 1/3 24 Independence Events A and B are independent iﬀ
P (A, B ) = P (A)P (B )
What are the alternate forms? 25 Independence Events A and B are independent iﬀ
P (A, B ) = P (A)P (B )
What are the alternate forms?
P (A) = P (AB )
P (B ) = P (B A) 26 Jochen Triesch’s famous pizza slide (modiﬁed from B. Warner) Free Pizza! Venn diagrams in
Pizza form from
B. Warner Statistical Independence:
P(A,B) = P(A)P(B)
or equivalently: P(AB) = P(A)
or equivalently: P(BA) = P(B) Pick slice at random!
What is P(pepperoni) ?
What is P(mushroom) ?
What is P(pepperoni  mushroom) ?
What is P(mushroom  pepperoni) ?
What is P(mushroom, pepperoni) ? 27 mushroom and pepperoni
events are independent! 28 Conditional Independence Venn diagrams in
Pizza form from
B. Warner Conditional
Independence:
P(A,BC) = P(AC)P(BC) Are the presence of mushrooms
P(mushroom, anchovy  pepperoni): and anchovies x 1/5 NO!
1/5 = 3/5 independent given pepperoni
P(mushroom, =epperoni  anchovy):
1/3 = 2/3 x 1/3 NO!
P (M P ) p ?
P(anchovy, pepperoni  mushroom):
1/4 = 2/4 x 3/4 NO!
Quiz: come up with pizza that has conditional independence
Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch 12 29 Conditional Independence Venn diagrams in
Pizza form from
B. Warner Conditional
Independence:
P(A,BC) = P(AC)P(BC) Are the presence of mushrooms
P(mushroom, anchovy  pepperoni): and anchovies x 1/5 NO!
1/5 = 3/5 independent given pepperoni
P(mushroom, =epperoni  anchovy):
1/3 = 2/3 x 1/3 NO!
P (M P ) p 3/5
P(anchovy, pepperoni  mushroom):
1/4 = 2/4 x 3/4 NO!
Quiz: come up with pizza that has conditional independence
Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch 12 30 Conditional Independence Venn diagrams in
Pizza form from
B. Warner Conditional
Independence:
P(A,BC) = P(AC)P(BC) Are the presence of mushrooms
P(mushroom, anchovy  pepperoni): and anchovies x 1/5 NO!
1/5 = 3/5 independent given pepperoni
P(mushroom, =epperoniAP ) = ?
1/3 = 2/3 x 1/3 NO!
P (M P ) p 3/5 P (  anchovy):
P(anchovy, pepperoni  mushroom):
1/4 = 2/4 x 3/4 NO!
Quiz: come up with pizza that has conditional independence
Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch 12 31 Conditional Independence Venn diagrams in
Pizza form from
B. Warner Conditional
Independence:
P(A,BC) = P(AC)P(BC) Are the presence of mushrooms
P(mushroom, anchovy  pepperoni): and anchovies x 1/5 NO!
1/5 = 3/5 independent given pepperoni
P(mushroom, =epperoniAP ) = 1/5 P (A, 1/3P ) /3 ? 1/3 NO!
P (M P ) p 3/5 P (  anchovy):
M = 2= x
P(anchovy, pepperoni  mushroom):
1/4 = 2/4 x 3/4 NO!
Quiz: come up with pizza that has conditional independence
Jochen Triesch, UC San Diego, http://cogsci.uc...
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This note was uploaded on 02/09/2014 for the course COGS 109 taught by Professor Staff during the Fall '08 term at UCSD.
 Fall '08
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