Probability - Caltech

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Independent events ! Two random events A, B are independent iff ! Events A 1 , A 2 , …, A n are independent iff
Interpreta)on of probabili)es ! Philosophical debate.. ! Frequen)st interpreta)on ! P(ω) is rela)ve frequency of ω in repeated experiments ! Ocen difficult to assess with limited data ! Bayesian interpreta)on ! P(ω) is “degree of belief” that ω will occur ! Where does this belief come from? ! Many different flavors (subjec)ve, objec)ve, pragma)c, …) ! For now assume probabili)es are known 11
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: Why use probabili)es? Related ev
Page 13 and 14: Examples ! Bernoulli distribu)on:
Page 15 and 16: Example: Gaussian distribu)on !
Page 17 and 18: Example: Mul)variate Gaussian 17
Page 19 and 20: Marginal distribu)ons What is P(
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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