# Lecture15 - CS440/ECE448 Intro to Articial Intelligence...

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Lecture 15: Probability review Bayes Nets intro Prof. Julia Hockenmaier [email protected] http://cs.illinois.edu/fa11/cs440 CS440/ECE448: Intro to ArtiFcial Intelligence What is the probability of…? 2 P( ) = 2/15 P( blue ) = 5/15 P( blue | ) = 2/5 P( ) = 1/15 P( red ) = 5/15 P( ) = 5/15 P( or ) = 2/15 P( | red ) = 3/5 Some terminology… Trial: e.g. picking a shape Sample space ! : the set of all possible outcomes (e.g. all kinds of shapes) Event " ˧ ! : an actual outcome of a trial (a subset of ! ) 3 CS440/ECE448: Intro AI Coin tossing Bernoulli distribution: Probability of success ( head ) in single yes/no trial The probability of head is p . The probability of tail is 1 p . Binomial distribution: Prob. of getting k heads in n independent yes/no trials 4

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Rolling a die Categorical distribution: Prob. of getting one of K outcomes in a single trial The probability of outcome c i is p i ( ! p i = 1 ) Multinomial distribution: Prob. of observing each possible outcome c i exactly x i times in a sequence of n yes/no trials 5 Laws of probability Ω B 6 CS440/ECE448: Intro AI A A ˬ B P( ! ) = 1 ˲ A ! : 0 P(A) 1 ˲ A,B ! : P(A B) P(A) ˲ A,B ! : P(A B) = P(A) + P(B) – P(A B) Random variables A function which maps every element in the sample space to some value. Boolean random variables: heads or tails? Categorical random variables: color, shape Continuous random variables: size, height,… 7 ¬A Discrete random variables The possible outcomes of discrete random variables (=atomic events) partition the sample space 8 CS440/ECE448: Intro AI A red yellow blue
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## This note was uploaded on 10/13/2011 for the course CS 440 taught by Professor Levinson,s during the Spring '08 term at University of Illinois, Urbana Champaign.

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Lecture15 - CS440/ECE448 Intro to Articial Intelligence...

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