A 3 x 3 stochastic matrix that describes the following situation. A college cafeteria offers three choices of dessert for lunch: ice cream (I), cake (C), and pie (P). A study of the students who order dessert every day showed that, of those students who order I on a certain day, the next day 60% of these students will order I and the others will be equally likely to order C or P. Of the students who order C on a certain day, the next day 40% of these students will order C and the others will be equally likely to order I or P. Of the students who order P on a certain day, the next day 80% of these students will order P and the others will be equally likely to order I or C.

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Answer 1

Question

Chapter 8.1, Problem 34E

(a)

To determine

To calculate: A 3 x 3 stochastic matrix that describes the following situation.

A college cafeteria offers three choices of dessert for lunch: ice cream (I), cake (C), and pie (P). A study of the students who order dessert every day showed that, of those students who order I on a certain day, the next day 60% of these students will order I and the others will be equally likely to order C or P. Of the students who order C on a certain day, the next day 40% of these students will order C and the others will be equally likely to order I or P. Of the students who order P on a certain day, the next day 80% of these students will order P and the others will be equally likely to order I or C.

(b)

To determine

To calculate: The percent of the students that will order cake tomorrow and the day after tomorrow. Given that today 20% of the students ordered ice cream, 30% ordered cake, and 50% ordered pie.

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Answer 2

Question

Chapter 8.1, Problem 34E

(a)

To determine

To calculate: A 3 x 3 stochastic matrix that describes the following situation.

A college cafeteria offers three choices of dessert for lunch: ice cream (I), cake (C), and pie (P). A study of the students who order dessert every day showed that, of those students who order I on a certain day, the next day 60% of these students will order I and the others will be equally likely to order C or P. Of the students who order C on a certain day, the next day 40% of these students will order C and the others will be equally likely to order I or P. Of the students who order P on a certain day, the next day 80% of these students will order P and the others will be equally likely to order I or C.

(b)

To determine

To calculate: The percent of the students that will order cake tomorrow and the day after tomorrow. Given that today 20% of the students ordered ice cream, 30% ordered cake, and 50% ordered pie.

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Answer 3

Question

Chapter 8.1, Problem 34E

(a)

To determine

To calculate: A 3 x 3 stochastic matrix that describes the following situation.

A college cafeteria offers three choices of dessert for lunch: ice cream (I), cake (C), and pie (P). A study of the students who order dessert every day showed that, of those students who order I on a certain day, the next day 60% of these students will order I and the others will be equally likely to order C or P. Of the students who order C on a certain day, the next day 40% of these students will order C and the others will be equally likely to order I or P. Of the students who order P on a certain day, the next day 80% of these students will order P and the others will be equally likely to order I or C.

(b)

To determine

To calculate: The percent of the students that will order cake tomorrow and the day after tomorrow. Given that today 20% of the students ordered ice cream, 30% ordered cake, and 50% ordered pie.

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Answer 4

Question

Chapter 8.1, Problem 34E

(a)

To determine

To calculate: A 3 x 3 stochastic matrix that describes the following situation.

A college cafeteria offers three choices of dessert for lunch: ice cream (I), cake (C), and pie (P). A study of the students who order dessert every day showed that, of those students who order I on a certain day, the next day 60% of these students will order I and the others will be equally likely to order C or P. Of the students who order C on a certain day, the next day 40% of these students will order C and the others will be equally likely to order I or P. Of the students who order P on a certain day, the next day 80% of these students will order P and the others will be equally likely to order I or C.

(b)

To determine

To calculate: The percent of the students that will order cake tomorrow and the day after tomorrow. Given that today 20% of the students ordered ice cream, 30% ordered cake, and 50% ordered pie.

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Answer 5

Chapter 8.1, Problem 34E

(a)

To determine

To calculate: A 3 x 3 stochastic matrix that describes the following situation.

A college cafeteria offers three choices of dessert for lunch: ice cream (I), cake (C), and pie (P). A study of the students who order dessert every day showed that, of those students who order I on a certain day, the next day 60% of these students will order I and the others will be equally likely to order C or P. Of the students who order C on a certain day, the next day 40% of these students will order C and the others will be equally likely to order I or P. Of the students who order P on a certain day, the next day 80% of these students will order P and the others will be equally likely to order I or C.

(b)

To determine

To calculate: The percent of the students that will order cake tomorrow and the day after tomorrow. Given that today 20% of the students ordered ice cream, 30% ordered cake, and 50% ordered pie.

Answer 6

Chapter 8.1, Problem 34E

(a)

To determine

To calculate: A 3 x 3 stochastic matrix that describes the following situation.

A college cafeteria offers three choices of dessert for lunch: ice cream (I), cake (C), and pie (P). A study of the students who order dessert every day showed that, of those students who order I on a certain day, the next day 60% of these students will order I and the others will be equally likely to order C or P. Of the students who order C on a certain day, the next day 40% of these students will order C and the others will be equally likely to order I or P. Of the students who order P on a certain day, the next day 80% of these students will order P and the others will be equally likely to order I or C.

Answer 7

Chapter 8.1, Problem 34E

(a)

To determine

To calculate: A 3 x 3 stochastic matrix that describes the following situation.

A college cafeteria offers three choices of dessert for lunch: ice cream (I), cake (C), and pie (P). A study of the students who order dessert every day showed that, of those students who order I on a certain day, the next day 60% of these students will order I and the others will be equally likely to order C or P. Of the students who order C on a certain day, the next day 40% of these students will order C and the others will be equally likely to order I or P. Of the students who order P on a certain day, the next day 80% of these students will order P and the others will be equally likely to order I or C.

Answer 8

(b)

To determine

To calculate: The percent of the students that will order cake tomorrow and the day after tomorrow. Given that today 20% of the students ordered ice cream, 30% ordered cake, and 50% ordered pie.

Answer 9

(b)

To determine

To calculate: The percent of the students that will order cake tomorrow and the day after tomorrow. Given that today 20% of the students ordered ice cream, 30% ordered cake, and 50% ordered pie.

Answer 10

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Answer 11

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Answer 12

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Answer 13

Ch. 8.1 - 1. Is a stochastic matrix? Ch. 8.1 - 2. Learning Process An elementary learning process...Ch. 8.1 - In Exercises 1-6, determine whether or not the...Ch. 8.1 - In Exercises 1-6, determine whether or not the...Ch. 8.1 - In Exercises 1-6, determine whether or not the...Ch. 8.1 - Prob. 4E Ch. 8.1 - In Exercises 1-6, determine whether or not the...Ch. 8.1 - Prob. 6E Ch. 8.1 - In Exercises 7–12, write a stochastic matrix...Ch. 8.1 - Prob. 8E

Solution Summary: The author calculates a 3 x 3 stochastic matrix that describes the following situation: A college cafeteria offers three choices of dessert for lunch: ice cream, cake, and pie.

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To calculate: The percent of the students that will order cake tomorrow and the day after tomorrow. Given that today 20% of the students ordered ice cream, 30% ordered cake, and 50% ordered pie.

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