Profits at a securities firm are determined by the volume of securities sold, and this volume fluctuates from week to week. If volume is high this week, then next week it will be high with a probability of 0.7 and low with a probability of 0.3. If volume is low this week then it will be high next week with a probability of 0.2.
Profits at a securities firm are determined by the volume of securities sold, and this volume fluctuates from week to week. If volume is high this week, then next week it will be high with a probability of 0.7 and low with a probability of 0.3. If volume is low this week then it will be high next week with a probability of 0.2.
Linear Algebra: A Modern Introduction
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ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
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12. Robots have been programmed to traverse the maze shown in Figure 3.28 and at each junction...
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![Profits at a securities firm are determined by the volume of securities sold, and this volume
fluctuates from week to week. If volume is high this week, then next week it will be high with a
probability of 0.7 and low with a probability of 0.3. If volume is low this week then it will be high
next week with a probability of 0.2.
1. Find the transition matrix for the Markov chain, with high volume being state 1 and low
volume state 2.
...
...
2. If the volume was low last week, what is the probability the volume will be low this week?
3. If the volume was high this week, what is the probability it will be low three weeks from
now?
4. If the volume was high this week, what is the probability it will be alternate between low
and high for the next three weeks (i.e. High → Low
→ High
Low.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fac73edbf-297f-4aed-9f9e-4c41e8d7aed8%2F33d32674-790e-429d-b9f6-46410833ec83%2Fcjhto76_processed.png&w=3840&q=75)
Transcribed Image Text:Profits at a securities firm are determined by the volume of securities sold, and this volume
fluctuates from week to week. If volume is high this week, then next week it will be high with a
probability of 0.7 and low with a probability of 0.3. If volume is low this week then it will be high
next week with a probability of 0.2.
1. Find the transition matrix for the Markov chain, with high volume being state 1 and low
volume state 2.
...
...
2. If the volume was low last week, what is the probability the volume will be low this week?
3. If the volume was high this week, what is the probability it will be low three weeks from
now?
4. If the volume was high this week, what is the probability it will be alternate between low
and high for the next three weeks (i.e. High → Low
→ High
Low.)
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