MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Solve bout the volume of securities sold by a brokerage firm, using the following data:
![**Markov Process Problem Set**
In this exercise, we are examining a Markov process involving weekly volume states. The states are defined as follows:
- **State 1**: High Volume
- **State 2**: Low Volume
Given the following transition probabilities:
(i) If the volume is high this week, next week it will be high with a probability of 0.9 and low with a probability of 0.1.
(ii) If the volume is low this week, next week it will be high with a probability of 0.3 and low with a probability of 0.7.
**Tasks:**
1. **Transition Matrix Construction**: Construct the transition matrix \( P \) for this Markov process.
\[
P = \begin{bmatrix}
\text{[Probability from state 1 to state 1]} & \text{[Probability from state 1 to state 2]} \\
\text{[Probability from state 2 to state 1]} & \text{[Probability from state 2 to state 2]}
\end{bmatrix} = \begin{bmatrix}
0.9 & 0.1 \\
0.3 & 0.7
\end{bmatrix}
\]
2. **Two-Week Probability**: If the volume this week is high, find the probability that the volume will be high two weeks from now.
3. **Three Consecutive Weeks Probability**: What is the probability that the volume will be high for three consecutive weeks?
These questions engage your understanding of Markov processes and involve calculations with transition matrices to predict state changes over time.](https://content.bartleby.com/qna-images/question/4da1f4c8-4970-49e9-beef-0939f39f632e/bdfd0033-5272-4715-ab7e-29930f9d8a69/hf5ssqr_processed.png)
Transcribed Image Text:**Markov Process Problem Set**
In this exercise, we are examining a Markov process involving weekly volume states. The states are defined as follows:
- **State 1**: High Volume
- **State 2**: Low Volume
Given the following transition probabilities:
(i) If the volume is high this week, next week it will be high with a probability of 0.9 and low with a probability of 0.1.
(ii) If the volume is low this week, next week it will be high with a probability of 0.3 and low with a probability of 0.7.
**Tasks:**
1. **Transition Matrix Construction**: Construct the transition matrix \( P \) for this Markov process.
\[
P = \begin{bmatrix}
\text{[Probability from state 1 to state 1]} & \text{[Probability from state 1 to state 2]} \\
\text{[Probability from state 2 to state 1]} & \text{[Probability from state 2 to state 2]}
\end{bmatrix} = \begin{bmatrix}
0.9 & 0.1 \\
0.3 & 0.7
\end{bmatrix}
\]
2. **Two-Week Probability**: If the volume this week is high, find the probability that the volume will be high two weeks from now.
3. **Three Consecutive Weeks Probability**: What is the probability that the volume will be high for three consecutive weeks?
These questions engage your understanding of Markov processes and involve calculations with transition matrices to predict state changes over time.
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