This suggests considering the random variable xe agee

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Unformatted text preview: = P(F) = P(BHH) = 0.5 So P(B|HH) = P(B int HH) / P(BHH) = P(BHH) / P(HH) = 0.5 / P(HH). But what is P(HH)? HH = BHH u FHH, so P(HH) = P(FHH) + P(BHH) = 1/8 + 1/2 = 5/8 So P(B|HH) = 0.5 / 5/8 = 4/5 = 0.80 = 80%  ­ Bayes Theorem: P(E'|E) = P(E|E') P(E') / P(E) Proof: P(E'|E) = P(E' int E) / PE) and P(E|E') = P(E' int E) / P(E'), so P(E' int E) = P(E) P(E'|E) = P(E') P(E|E') and thus P(E'|E) = P(E') P(E|E') / P(E)  ­ Random Variables: functions X:S  ­ ­> R  ­ Idea is that associated with an outcome there may be additional quantities of interest.  ­ Example: Suppose a social scientist suspects that a student's age plus their GPA is significant for their getting a summer job. This suggests considering the...
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This note was uploaded on 01/13/2012 for the course CMSC 250 taught by Professor Staff during the Summer '08 term at Maryland.

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