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CE311s-stw-lesson2-L

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CE311
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  LESSON 2  SAMPLE SPACE & EVENTS ã Experiment:  action or process that generates an observation (“value” of the outcome) ã The sample space  of an experiment, denoted by S  , is the set of all possible outcomes of an experiment. ã Examples? ã  An event  is any collection  of outcomes contained in a sample space S  . An event is a set . ã Simple & compound events.    SAMPLE SPACE & EVENTS ã Simple events consist of exactly one outcome ã Compound consist of more than one outcome ã Flip a quarter three times. ã 8 Simple outcomes  – {HHH} {HHT} {HTH} {THH} {HTT}  – {TTH} {THT} {TTT} ã Many compound outcomes  –  At least 2 Tails  – {HTT} {TTH} {THT} {TTT} ã Many Others  RELATIONS FROM SET THEORY ã The union  of two events  A    &    B    (A     B, A or B)   is an event consisting of all the outcomes that are    either in A or in B or in both events. ã The intersection  of two events  A &    B    (A    B, A & B)   is the event consisting of all outcomes that are in both A & B. ã The complement  of an event  A (A’)   is the set of all outcomes in S   that are not contained in A . ã If  A & B   have no   outcomes in common , they are mutually exclusive  or disjoint .
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