EC255 Lecture Notes - Lecture 5: Bayes Estimator, Mutual Exclusivity
Document Summary
Four laws of probability: laws enable to calculate probability of more complex events from probability of simpler events, law of addition, law of conditional probability, law of multiplication, bayes" rule. The general law of addition states that the probability of the union of two events a and b is. Do not count the two red aces twice! Involves mutually exclusive events: recall that events a and b are mutually exclusive if their intersection contains no elements, special law of addition is. If a (cid:1514) b = {}, then p(a (cid:1514) b) = 0: p(a (cid:1515) b) = p(a) + p(b) Conditional probability: conditional probability for events e1 and e2, the ratio of the relative size of e1 (cid:1514) e2 to e2 is. Law of multiplication: multiplication rule for two events e1 and e2, note: P(e2 | e1) = p(e2) and the law of multiplication simplifies to. Example: television ads: so, p(ad a) = 0. 25.
