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Redo exercises 7 and 8 in section 8.3 of your textbook, about the small animal who lives in an area with woods and meadows, using the following data: If the animal is in the woods on one observation, then it is four times as likely to be in the woods as the meadows on the next observation. If the animal is in the meadows on one observation, then it is as likely to be in the meadows as the woods on the next observation. Assume that state 1 is being in the meadows and that state 2 is being in the woods. (1) Find the transition matrix for this Markov process. P= (2) If the animal is twice as likely to be in the meadows as in the woods, find the state vector X that represents this information? (3) Using the state vector determined in the preceding part as the initial state vector, find the probability that the animal is in the meadow on the third observation after the initial one. (4) If the probability that the animal will be the meadow at a specific point in time is 0.05, how many subsequent observations must be made before the probability that it is in the meadow exceeds 0.2?

Redo exercises 7 and 8 in section 8.3 of your textbook, about the small animal who lives in an area with woods and meadows, using the following data: If the animal is in the woods on one observation, then it is four times as likely to be in the woods as the meadows on the next observation. If the animal is in the meadows on one observation, then it is as likely to be in the meadows as the woods on the next observation. Assume that state 1 is being in the meadows and that state 2 is being in the woods. (1) Find the transition matrix for this Markov process. P= (2) If the animal is twice as likely to be in the meadows as in the woods, find the state vector X that represents this information? (3) Using the state vector determined in the preceding part as the initial state vector, find the probability that the animal is in the meadow on the third observation after the initial one. (4) If the probability that the animal will be the meadow at a specific point in time is 0.05, how many subsequent observations must be made before the probability that it is in the meadow exceeds 0.2?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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Redo exercises 7 and 8 in section 8.3 of your textbook, about the small animal who lives in an area with woods and meadows, using the following data: If the animal is in the woods on one observation, then it is four times as likely to be in the woods as the meadows on the next observation. If the animal is in the meadows on one observation, then it is as likely to be in the meadows as the woods on the next observation. Assume that state 1 is being in the meadows and that state 2 is being in the woods. (1) Find the transition matrix for this Markov process. P = (2) If the animal is twice as likely to be in the meadows as in the woods, find the state vector X that represents this information? (3) Using the state vector determined in the preceding part as the initial state vector, find the probability that the animal is in the meadow on the third observation after the initial one. (4) If the probability that the animal will be the meadow at a specific point in time is 0.05, how many subsequent observations must be made before the probability that it is in the meadow exceeds 0.2?
Transcribed Image Text:Redo exercises 7 and 8 in section 8.3 of your textbook, about the small animal who lives in an area with woods and meadows, using the following data: If the animal is in the woods on one observation, then it is four times as likely to be in the woods as the meadows on the next observation. If the animal is in the meadows on one observation, then it is as likely to be in the meadows as the woods on the next observation. Assume that state 1 is being in the meadows and that state 2 is being in the woods. (1) Find the transition matrix for this Markov process. P = (2) If the animal is twice as likely to be in the meadows as in the woods, find the state vector X that represents this information? (3) Using the state vector determined in the preceding part as the initial state vector, find the probability that the animal is in the meadow on the third observation after the initial one. (4) If the probability that the animal will be the meadow at a specific point in time is 0.05, how many subsequent observations must be made before the probability that it is in the meadow exceeds 0.2?
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