18.44 Lecture Notes - Lecture 13: Prati, Ratia, Royal Institute Of Technology
Document Summary
Break choosing one of the items to be counted into a sequence of stages so that one always has the same number of choices to make at each stage. Then the total count becomes a product of number of choices available at each stage. Represent partition by k 1 bars and stars, e. g. , as | || | . P(a) [0,1] for all (measurable) a (cid:15468) s. Countable additivity: p( = e ) = p(e ) if e e =(cid:15477) for each pair i and j. Observe p(a b) = p(a) + p(b) p(ab). Also, p(e f g) = p(e) + p(f) + p(g) p(ef) p(eg) p(fg) + p(efg). More generally n people toss hats into a bin, randomly shuf e, return one hat to each person. Inclusion-exclusion: let e be the event that ith person gets own hat. There are terms like that in the inclusion exclusion sum.
