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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 0.8 and low with a probability of 0.2. 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? 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.)

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 0.8 and low with a probability of 0.2. 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? 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.)

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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 0.8 and low with a probability of 0.2. 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? 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.)
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 0.8 and low with a probability of 0.2. 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? 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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