investmenttool-probability6422.pptx

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1、Investment Tools ProbabilitySASF CFA Quant.Review1ProbabilityA random variable is a quantity whose outcome is uncertain.Two defining properties of Probability.1.Probability of any event E is a number between 0 and 1,p(E).2.Sum of the probabilities of any list of mutually exclusive and exhaustive eve

2、nts equals 1.Mutually exclusive=one and only one event can occur at any time.Exhaustive=one of the events must occur,jointly cover all possible outcomes.Empirical probability-probability of an event occurring is estimated from data,usually in the form of a relative frequency.A priori probability-pro

3、bability of an event is deduced by reasoning about the structure of the problem itself.Subjective probability-probability of an event is based on a personal assessment without reference to any particular data.2Visualizing Sample Space1.ListingS=Head,Tail2.Contingency Table3.Decision Tree Diagram32nd

4、 Coin1st CoinHead TailTotalHead HH HT HH,HTTail TH TT TH,TTTotal HH,TH HT,TT SContingency TableExperiment:Toss 2 Coins.Note Faces.S=HH,HT,TH,TT Sample SpaceOutcome(Count,Total%Shown Usually)SimpleEvent(Head on1st Coin)4Tree DiagramOutcome S=HH,HT,TH,TTSample SpaceExperiment:Toss 2 Coins.Note Faces.THTHTHHHTTHTTH5Second DieFirst DieProbabilities for Two Dice6