cs440-lec4-probability - CS 440 / ECE 448 Introduction to...

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Unformatted text preview: CS 440 / ECE 448 Introduction to Artificial Intelligence Spring 2008 Instructor: Eyal Amir Where we are in this class So far: propositional logic, matrix algebra Propositional logic: propositions, formulas, truth assignments, formula evaluation, entailment, CNF Matrix algebra: vectors, matrices, +, *, transpose, eigen vectors, eigen values, rank, inverse Today: Probability Random experiment, domain ( Ω ), events Example: Ω = {H,T} (coin) Example: Ω = {1,2,3,4,5,6} (die) Example: Ω = N N = {1,2,3,…} (e.g., time) Random Variables (RVs), Probability Distributions (P) This class: Discrete, finite domains Random Variables: Examples Random Variables: Examples X takes the value True (T) with probability p and False (F) with probability 1-p is a random variable with distribution (p,1-p) Formally: dom(X)={T,F}; P(X=T)=p; P(X=F)=1-p If an urn contains balls having 3 possible colors – red, yellow, and blue – the color of a ball picked at random from the bag is a random variable with 3 possible values The (probability) distribution of a random variable X with n values x 1 , x 2 , …, x n is: (p 1 , p 2 , …, p n ) with P(X=x i ) = p i and Σ i=1,…,n p i = 1 Expected Value Expected Value Random variable X with n values x 1 ,…,x n and distribution (p 1 ,…,p n ) E.g.: X is the state reached after doing an E....
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This note was uploaded on 05/04/2008 for the course CS 440 taught by Professor Eyalamir during the Spring '08 term at University of Illinois at Urbana–Champaign.

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cs440-lec4-probability - CS 440 / ECE 448 Introduction to...

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