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Slides Weed 6 and 7

Slides Weed 6 and 7 - BERNOULLI TRIALS(a very special and...

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BERNOULLI TRIALS (a very special and common type of selection experiment)
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EG1) The Attachment Disorder : Techston McCool has a serious attachment disorder. Each and every time he sends an email that requires an attachment, there is only a “p” percent chance that he will remember to include the attachment. Suppose an experiment consists of observing Techston send four email messages that are supposed to contain attachments, and each time we note whether or not he includes the attachment (S) or fails to include the attachment (F). QUESTION 1: What is the probability that Techston includes the attachment exactly three times? QUESTION 2: What is the probability that Techston includes the attachment exactly two times? QUESTION 3: What is the probability that Techston includes either two or three attachments?
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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 Attachment Disorder Pr[S] = p Pr[F] = q = 1-p ssss p4 sssf p3q1 ssfs p3q1 ssff p2q2 sfss p3q1 sfsf p2q2 sffs p2q2 sfff p1q3 fsss p3q1 fssf QUESTION 1: What is the probability that Techston includes the attachment exactly three times? QUESTION 2: What is the probability that Techston includes the attachment exactly two times? QUESTION 3: What is the probability that Techston includes either two or three attachments?
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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 ssss p4 sssf p3q1 ssfs p3q1 ssff p2q2 sfss p3q1 sfsf p2q2 sffs p2q2 sfff p1q3 fsss p3q1 fssf RED = “S” 3 times GREEN = “S” 2 times The Attachment Disorder Pr[S] = p Pr[F] = q = 1-p
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Q1) Pr[exactly 3 S’s] = Pr[ 3 S’s and 1 F ] = = Pr[ SSSF, SSFS, SFSS, FSSS ] = 4p3q1 Q2) Pr[exactly 2 S’s] = Pr[ 2 S’s and 2 F’s ] = = Pr[ SSFF, SFSF, SFFS, FSSF, FSFS, FFSS ] = 6p2q2 Q3) Pr[two S’s or three S’s] = Pr[ 2S & 2F or 3S & 1F ] = Pr[ SSFF, SFSF, SFFS, FSSF, FSFS, FFSS, SSSF, SSFS, SFSS, FSSS ] = 6p2q2 + 4p3q1
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BERNOULLI TRIALS An experiment consists of a sequence of Bernoulli trials if….
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