M118 Weeks 6 & 7

M118 Weeks 6 & 7 - ( E G 1 The Occasional...

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(a very special and specific kind of selection experiment)
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EG 1)   The Occasional Student The Occasional Student :  Eve ry da y, a n M118 s tude nt  (who m  I s ha ll c a ll “Bo b  Lo b la w”) ha s  pro b a b ility “p” o f s ho wing up to  c la s s .  An e xpe rim e nt c o ns is ts  o f m e  o b s e rving  this s tude nt’s  a tte nda nc e  o ve r fo ur c la s s  pe rio ds , no ting  e a c h  da y whe the r the  s tude nt s ho ws  up (S ) o r fa ils  to  s ho w up (F). a .)  Wha t is  the  pro b a b ility tha t Bo b  s ho ws  up e xa c tly thre e  tim e s ? b .)  Wha t is  the  pro b a b ility tha t Bo b  s ho ws  up e xa c tly two  tim e s ? c .)  Wha t is  the  pro b a b ility tha t Bo b  s ho ws  up                                            e ithe r two  tim e s  o r thre e  tim e s ?
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Start S F S F S F S F S F S F S F s F s F s F s F s F s F s F s F p q p q p q p q p q p q p q p q p q p q p q p q p q p q p q The occasional Student Pr[S] = p Pr[F] = q = 1-p ssss p 4 sssf p 3 q 1 ssfs p 3 q 1 ssff p 2 q 2 sfss p 3 q 1 sfsf p 2 q 2 sffs p 2 q 2 sfff p 1 q 3 fsss p 3 q 1 fssf p 2 q 2 fsfs p 2 q 2 fsff p 1 q 3 ffss p 2 q 2 ffsf p 1 q 3 fffs p 1 q 3 ffff q 4 a.)  What is the probability that Bob shows up  exactly three times ? b.)  What is the probability that Bob shows up  exactly two times ? c.)  What is the probability that Bob shows up   either  two times  or  three times ?
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Start S F S F S F S F S F S F S F s F s F s F s F s F s F s F s F p q p q p q p q p q p q p q p q p q p q p q p q p q p q p q The occasional Student Pr[S] = p Pr[F] = q = 1-p ssss p 4 sssf p 3 q 1 ssfs p 3 q 1 ssff p 2 q 2 sfss p 3 q 1 sfsf p 2 q 2 RED = “S” 3 times GREEN = “S” 2 times
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a.)  Pr[shows up 3 times] = Pr[ 3 S’s and 1 F ] =   = Pr[ SSSF, SSFS, SFSS, FSSS ] = 4p 3 q 1 b.)  Pr[shows up 2 times] = Pr[ 2 S’s and 2 F’s ] =  = Pr[ SSFF, SFSF, SFFS, FSSF, FSFS, FFSS  ] = 6p 2 q 2
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c.)  Pr[shows up 2 times or 3 times] = Pr[  or  ] = Pr[ SSFF, SFSF, SFFS, FSSF, FSFS, FFSS,  SSSF, SSFS, SFSS, FSSS 6p 2 q 2 +  4p 3 q 1     = Pr[shows up 2 times]+Pr[shows up 3 times]
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BERNOULLI TRIALS BERNOULLI TRIALS An experiment consists of a sequence of Bernoulli trials if…. An experiment consists of a sequence of Bernoulli trials if…. 1.)  at each selection, only two possible fixed outcomes 
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This note was uploaded on 01/24/2011 for the course MATH M118 taught by Professor Stevemckinley during the Fall '07 term at Indiana.

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M118 Weeks 6 & 7 - ( E G 1 The Occasional...

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