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Unformatted text preview: Administration 1. Midterm 2, Wednesday, November 9th. 810PM, 155 Dwinelle. 2. Extra office hours: Tuesday, November 8th, 49PM, 310 Soda. 3. No class on Wednesday!! CS70: Satish Rao: Lecture 30. 1. Review Joint distribution, conditional expectation. 2. Conditional Independence. 3. Inference. Joint Distributions. For random variables, X and Y the joint distribution is Pr [ X = a , Y = b ] for each possible a , b . Joint Distributions. For random variables, X and Y the joint distribution is Pr [ X = a , Y = b ] for each possible a , b . Marginal Distributions are the distibutions of X and Y . ( Pr [ X = a ] = b Pr [ X = a , Y = b ] . ) Joint Distributions. For random variables, X and Y the joint distribution is Pr [ X = a , Y = b ] for each possible a , b . Marginal Distributions are the distibutions of X and Y . ( Pr [ X = a ] = b Pr [ X = a , Y = b ] . ) Conditional Expectation of X given event A ] E ( X  A ) = a a Pr [ X = a  A ] . Joint Distributions. For random variables, X and Y the joint distribution is Pr [ X = a , Y = b ] for each possible a , b . Marginal Distributions are the distibutions of X and Y . ( Pr [ X = a ] = b Pr [ X = a , Y = b ] . ) Conditional Expectation of X given event A ] E ( X  A ) = a a Pr [ X = a  A ] . Total Expectation Law: E ( X ) = b Pr [ Y = b ] E ( X  Y = b ) . Conditional independence. Events A and B are conditionally independent given C if Pr [ A , B  C ] = Pr [ A  C ] Pr [ B  C ] . or Pr [ A  B , C ] = Pr [ A  C ] . Example: roll 3 die. Conditional independence. Events A and B are conditionally independent given C if Pr [ A , B  C ] = Pr [ A  C ] Pr [ B  C ] . or Pr [ A  B , C ] = Pr [ A  C ] . Example: roll 3 die. A sum of first two greater than 7 Conditional independence. Events A and B are conditionally independent given C if Pr [ A , B  C ] = Pr [ A  C ] Pr [ B  C ] . or Pr [ A  B , C ] = Pr [ A  C ] . Example: roll 3 die. A sum of first two greater than 7 B sum of first and third is greater than 7 Conditional independence. Events A and B are conditionally independent given C if Pr [ A , B  C ] = Pr [ A  C ] Pr [ B  C ] . or Pr [ A  B , C ] = Pr [ A  C ] . Example: roll 3 die. A sum of first two greater than 7 B sum of first and third is greater than 7 C first one is 5 A and B are not independent. Conditional independence. Events A and B are conditionally independent given C if Pr [ A , B  C ] = Pr [ A  C ] Pr [ B  C ] . or Pr [ A  B , C ] = Pr [ A  C ] . Example: roll 3 die. A sum of first two greater than 7 B sum of first and third is greater than 7 C first one is 5 A and B are not independent....
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This note was uploaded on 02/29/2012 for the course COMPSCI 70 taught by Professor Rau during the Fall '11 term at University of California, Berkeley.
 Fall '11
 Rau

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