Prior probability Prior or unconditional probabilities of propositions e.g.,P(Cavity true)=0.1 and P(Weather=sunny)=0.72 correspond to belief prior to arrival of any(new)evidence Probability distribution gives values for all possible assignments: P(Weather)=<0.72,0.1,0.08,0.1>(normalized,i.e.,sums to 1) Joint probability distribution for a set of random variables gives the probability of every atomic event on those random variables P(Weather,Cavity)=a 4X 2 matrix of values: Weather= sunny rainy cloudy snow Cavity true 0.144 0.02 0.016 0.02 Cavity false 0.576 0.08 0.0640.08Prior probability • Prior or unconditional probabilities of propositions • e.g., P(Cavity = true) = 0.1 and P(Weather = sunny) = 0.72 correspond to belief prior to arrival of any (new) evidence • Probability distribution gives values for all possible assignments: • P(Weather) = <0.72,0.1,0.08,0.1> (normalized, i.e., sums to 1) • Joint probability distribution for a set of random variables gives the probability of every atomic event on those random variables • P(Weather,Cavity) = a 4 × 2 matrix of values: Weather = sunny rainy cloudy snow Cavity = true 0.144 0.02 0.016 0.02 Cavity = false 0.576 0.08 0.064 0.08 • Every question about a domain can be answered by the joint distribution