2. Probability Notation Review Prior (unconditional) probability is before evidence is obtained, after is posterior or conditional probability P(A) – Prior – only valid when no other info is available Random variable P(X=pizza), X has a domain and  P(x i )=1 (note that variables are by convention in caps in probability theory) Probability distribution – P(X) vector (for discrete vars) of probabilities of domain of X. Sums to 1. Can use standard connectives, i.e. P(A  B) P(A|B) – conditional probability – probability of A given B As soon as we know C we should use P(A|B  C) P(A|B) = P(A  B)/P(B) Product rule: P(A  B) = P(A|B)P(B) = P(B|A)P(A) P(A  B) = P(A) + P(B) – P(A  B) – venn diagram P(A) + P(!A) = 1 Joint probability table (JPT): Table that shows all of the probabilities for all possible events

5. Independence