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The SKI-HI Junk Bond Company classifies each week's sales volume as high (H) or very high (V). Data indicates that the week-to-week changes in volume follow the pattern of a Markov chain with states H and V and the transition probabilities are as follows: Transition Probability H+H 3 H+V .7 V+H 5 5 If the current week's volume is high (H), what is the probability that it will be very high (V) 3 weeks from now? a) 56 b) 588 c) 4 d) A12 e) none of the others

The SKI-HI Junk Bond Company classifies each week's sales volume as high (H) or very high (V). Data indicates that the week-to-week changes in volume follow the pattern of a Markov chain with states H and V and the transition probabilities are as follows: Transition Probability H+H 3 H+V .7 V+H 5 5 If the current week's volume is high (H), what is the probability that it will be very high (V) 3 weeks from now? a) 56 b) 588 c) 4 d) A12 e) none of the others

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
Problem 9EQ
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Please answer #23 and explain your reasoning!
| 14 3/4" L 118 7/8 be the transition matrix for a regular Markov chain. Find w2, the second 20 Let P= coordinate of the stable vector for this Markov chain. a) 67 b) 17 c) 18 d) 7/8 e) none of the others 21. Let E, F, and G be events in a sample space S and suppose Pr[E] = Pr[F] = Pr[G] = .5, PrEOFOG] = PHE'OFOG]= PHE nF n Gʻ) = 2, and Pr[EnFnG]=.1. What is a) 2 b) 1 c) not enough information d) 3 e) none of the others 22 Sam's Sub Shoppe uses a linear relationship, based on length, to determine the selling price of a sub sandwich. If a 5 inch sub sells for $3.50 and an 8 inch sub sells for $5.30, what is the price of a two-foot sub? a) $15.90 b) $16.90 e) $19.95 d) $14.90 e) none of the others 23 The SKI-HI Junk Bond Company classifies each week's sales volume as high (H) or very high (V). Data indicates that the week-to-week changes in volume follow the pattern of a Markov chain with states H and V and the transition probabilities are as follows: Transition Probability H→H 3 H+ V .7 V+H 5 V → V If the current week's volume is high (H), what is the probability that it will be very high (V) 3 weeks from now? a) 56 b) 588 c) 4 d) 412 e) none of the others 24. A company buys 9 computers, and it plans to connect each pair of computers by a cable (one cable per pair). How many cables are needed? a) 18 b) 72 c) 9! d) 36 e) none of the others 25. A bucket contains 3 red balls and 2 blue balls. Two balls are drawn simultaneously and at random. What is the probability that one ball is blue, given that at least one ball is red? a) 13 b) 23 c) 25 d) 35 e) none of the others
Transcribed Image Text:| 14 3/4" L 118 7/8 be the transition matrix for a regular Markov chain. Find w2, the second 20 Let P= coordinate of the stable vector for this Markov chain. a) 67 b) 17 c) 18 d) 7/8 e) none of the others 21. Let E, F, and G be events in a sample space S and suppose Pr[E] = Pr[F] = Pr[G] = .5, PrEOFOG] = PHE'OFOG]= PHE nF n Gʻ) = 2, and Pr[EnFnG]=.1. What is a) 2 b) 1 c) not enough information d) 3 e) none of the others 22 Sam's Sub Shoppe uses a linear relationship, based on length, to determine the selling price of a sub sandwich. If a 5 inch sub sells for $3.50 and an 8 inch sub sells for $5.30, what is the price of a two-foot sub? a) $15.90 b) $16.90 e) $19.95 d) $14.90 e) none of the others 23 The SKI-HI Junk Bond Company classifies each week's sales volume as high (H) or very high (V). Data indicates that the week-to-week changes in volume follow the pattern of a Markov chain with states H and V and the transition probabilities are as follows: Transition Probability H→H 3 H+ V .7 V+H 5 V → V If the current week's volume is high (H), what is the probability that it will be very high (V) 3 weeks from now? a) 56 b) 588 c) 4 d) 412 e) none of the others 24. A company buys 9 computers, and it plans to connect each pair of computers by a cable (one cable per pair). How many cables are needed? a) 18 b) 72 c) 9! d) 36 e) none of the others 25. A bucket contains 3 red balls and 2 blue balls. Two balls are drawn simultaneously and at random. What is the probability that one ball is blue, given that at least one ball is red? a) 13 b) 23 c) 25 d) 35 e) none of the others
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