Probability Notation Review

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 <x1, x2,…> and P(xi)=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