Popular in Statistics I
Popular in Statistics
This 0 page Class Notes was uploaded by Jacob Decker on Wednesday November 4, 2015. The Class Notes belongs to STT 421 at Michigan State University taught by v. melfi in Fall 2015. Since its upload, it has received 21 views. For similar materials see Statistics I in Statistics at Michigan State University.
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Date Created: 11/04/15
William Decker A46084250 STT421 1 1115 STT 421 Homework 4 Exercises 4119 4127 4128 511 527 from the text Exercises 5 8 12 13 14 from the Extra Notes on Probability on the course web site For Exercise 5 27b use R For other exercises you don t need to use R 0 4119 Conditional probabilities and independence 125175 186 210 06722 b Pin labor force I college graduate 4041451568 07837 c No since Pin labor force I college graduate does not equal Pin labor a Pin labor force force 0 4127 Cystic fibrosis 0 Pcarries gene 125 Assuming that we are only considering someone from European ancestry from this point on O Ppositive test carries gene 09 O Ppositive not carries gene 0 O Pcarries gene positive test 1 lt2 5lto9gt O Pcarries gene positive test 1 1 24 09lt 0 25 25 0 4128 Use Bayes s rule 0 PJulianne PCarrier 23 0 Pcystic carrier 14 0 Pcystic not carrier 0 O Pcarrier no cystic Pcarrier and cysticPno cystic 2334 2334131 0396001 0 511 Should you use the binomial distribution a Let X denote the number of word errors out of the 10 in the essay that are caught Then X Bnp Where n 10 and p 07 The distribution for X is then given by mm lko 07k0310k for k 012 10 0 Similarly if Y denotes the number of errors missed then Y B1003 and Pyk 1k0 03k071039k for k 012 10 b We want PY 2 4This is the same as 1PY S 3 or 1 Fy3 Where Fy is the cumulative distribution function of Y Using R to estimate PY 2 4 we obtain Y 2 4 1 pbinom31003 z 035 or about 35 0 527 A test for ESP a Probability of correctly identifying the shape on a card by just guessing is 14 or 025 b In 20 trials the number of correct identifications X has the binomial distribution With n 20 and p 025 The probability that the subject guesses at least 10 of the 20 shapes PX210 1 PXS9 1 binomialcdfn p k 1 binomialcdf20 25 9 1 09861 001386 or approximately 139 c ux np 20025 5 OX SQRTnp1P SQRT20O25075 19365 d The binomial model does not apply if the 25 cards are opened one at a time The binomial model applies only if the card is put back in the deck and the deck is shuf ed before drawing the next card Exercise 5 M1 first armadillo chosen is male F1 first armadillo chosen is female M2 second armadillo chosen is male F2 second armadillo chosen is male a PF1 and F2 PF2 F1PF1 719820 1495 01474 or 1474 b Do not choose the same armadillo twice gt without replacement Does not matter whether a female is chosen first and a male is chosen second or a male is chosen first and a female is chosen second PF M PM F 9251624 1625924 288600 1225 048 OR P1 F and 1 M 9C116C125C2 96300 144300 1225 048 Exercise 8 Sensitivity is the probability that an email will go to spam among spam emails The PPV is dependent on how many emails are spam Exercise 12 a Truth Flagged Not agged Person has weapon 0995 0005 Person has no weapon 085 015 b PPV 09950995 085 05393 c NPV 015015 0005 09677 d The NPV is more important because of the low prevalence of non agged weapon carriers Exercise 13 0348 0252 06 or 60 Exercise 14 a 00297 00065 00362 or 362 b 0065 or 065 c 018 or 18
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