probnotes

probnotes - Summary Notes - Probability Theory Basic...

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Summary Notes - Probability Theory Basic De…nitions De…nition 1 The term probability refers to the study of randomness and uncertainty. In any situation in which one of a number of possible outcomes may occur, the theory of probability provides methods for quantifying the chances, or likelihoods, associated with the various outcomes. De…nition 2 An experiment is any action or process that generates observations. De…nition 3 The sample space of an experiment, denoted by S , is the set of all possible outcomes of the experiment. De…nition 4 An event is any collection (subset) of outcomes contained in the sample space S . An event is said to be simple if it consists of exactly one outcome and compound if it consists of more than one outcome. De…nition 5 The union of two events A and B , denoted by A [ B and read ” A or B ,” is the event consisting of all outcomes that are either in A or in B or in both events (so that the union includes outcomes for which both A and B occur as well as outcomes for which exactly one occurs). De…nition 6 The intersection of two events A and B , denoted by A \ B (sometimes AB ) and read ” A and B ,” is the event consisting of all outcomes that are in both A and B . De…nition 7 The complement of an event A , denoted by A 0 (sometimes A c or A ), is the set of all outcomes in S that are not contained in A . De…nition 8 When A and B have no outcomes in common, they are said to be mutually exclu- sive or disjoint events. Elementary Laws from Set Theory Commutative Laws E [ F = F [ E ; E \ F = F \ E . Associative Laws E [ ( F [ G ) = ( E [ F ) [ G ; E \ ( F \ G ) = ( E \ F ) \ G . Distributive Laws ( E \ F ) [ G = ( E [ G ) \ ( F [ G ) ; ( E [ F ) \ G = ( E \ G ) [ ( F \ G ) DeMorgan’s First Law à n [ i =1 E i ! 0
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probnotes - Summary Notes - Probability Theory Basic...

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