Probability - Caltech

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Probabilis)c proposi)onal logic ! Suppose we would like to express uncertainty about logical proposi)ons ! Birds can typically fly ! Proposi)onal symbols Bernoulli random variables ! Specify for all ! Events encode assignments to all proposi)onal symbols ! <strong>Probability</strong> of a proposi)on φ is the probability mass of all models of φ (i.e., all ω that make φ true) 18
Marginal distribu)ons What is P(Toothache)? Joint distribu)on 19
Page 1 and 2: Introduc)on to Ar)ficial Intellig
Page 3 and 4: Announcements ! Grading: AvianAske
Page 5 and 6: Quan)fying Uncertainty ! So far,
Page 7 and 8: Decision making under uncertaint
Page 9 and 10: Why use probabili)es? Related ev
Page 11 and 12: Interpreta)on of probabili)es ! P
Page 13 and 14: Examples ! Bernoulli distribu)on:
Page 15 and 16: Example: Gaussian distribu)on !
Page 17: Example: Mul)variate Gaussian 17
Page 21 and 22: Condi)onal distribu)ons ! Formal
Page 23 and 24: Posterior inference ! Suppose we
Page 25 and 26: Independent RVs ! What if RVs a

Probability - Caltech

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