ENEE 324 Lecture Notes - Lecture 1: Disjoint Sets, Conditional Independence, Sample Space
8 Mar 2018
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1 probability spaces: a probability space is a triplet ( ,f , p) where is a sample space, f is a -algebra and and p is a probability measure, the sample space, contains all possible outcomes. 2 axioms of probability: given a sample space and events a, b, p(a) 0, a , p(a b) = p(a) + p(b) if a b = . Furthermore, if {ai} i=1 has pairwise disjoint elements then p( P(b) (read as p(a given b): def: a partition of is a set {bj}n j=1 of disjoint events such that. Sj=1: total law of probability: given a sample space , an event a and a partition{bj}n j=1 of : P(a|bj)p(bj: bayes theorem: given a sample space , an event a and a partition {bj}n j=1 of : Proof follows trivially from de nitions of conditional probability and total law of. Probability: multiplication rule: given a set of events {ai}n i=1:
