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 0.1. 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? ...

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.5: Markov Chain
Problem 31E
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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 0.1.
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?
...
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 0.1. 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? ...
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