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USC BUAD 310 - Business Stat Lecture 2

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Set Operations – Venn DiagramComplement – complement of A, denoted by Ac is the event consisting of all outcomes that are not contained in A.Union – union of A and B, denoted by A U B, is the event consisting of all outcomes that are either in A or B.Intersection – intersection of A and B, denoted by A (upside down U) B, is event consisting of all outcomes that are in both A and B.A and B are said to be disjoint or mutually exclusive if A and B have no outcomes in commonRelative Frequency – proportion measuring how often, or how frequently, the event occurs in a sequence of experimentsEx: experiment of tossing a coin – if experiment is repeate many times, the relative frequency of heads will usually be close to ½Law of Large Numbers (LLN) – relative frequency of an outcome converges to a number, probability of the outcome, as the number of repeated experiments increase.Subjective/Personal Probability – measures an individual’s belief in the statement he/she is making.Ex: “What is the probability that the Lakers will win the NBA final this year?” – hard to interpret such a probability using frequency interpretation because basketball season can only be played once.P(E) = Number of outcomes in event ENumber of outcomes in sample space S- probability of event E equals proportion of outcomes in sample space contained in E.Business Stat Lecture 2 01/24/2012Set Operations – Venn DiagramComplement – complement of A, denoted by Ac is the event consisting of all outcomes that are not contained in A.Union – union of A and B, denoted by A U B, is the event consisting of all outcomes that are either in A or B.Intersection – intersection of A and B, denoted by A (upside down U) B, is event consisting of all outcomes that are in both A and B.A and B are said to be disjoint or mutually exclusive if A and B have no outcomes in commonRelative Frequency – proportion measuring how often, or how frequently, the event occurs in a sequence of experimentsEx: experiment of tossing a coin – if experiment is repeate many times,the relative frequency of heads will usually be close to ½Law of Large Numbers (LLN) – relative frequency of an outcome converges to a number, probability of the outcome, as the number of repeated experiments increase.Subjective/Personal Probability – measures an individual’s belief inthe statement he/she is making.Ex: “What is the probability that the Lakers will win the NBA final this year?” – hard to interpret such a probability using frequency interpretation because basketball season can only be played once.P(E) = Number of outcomes in event E  Number of outcomes in sample space S- probability of event E equals proportion of outcomes in sample space contained in


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