(1) If volume is high this week, then next week it will be high with a probability of 0.9 and low with a probability of (ii) If volume is low this week then it will be high next week with a probability of 0.5. Assume that state 1 is high volume and that state 2 is low volume. (Note: Express your answers as decimal fractions rounded to 4 decimal places (if they have more than 4 decimal
(1) If volume is high this week, then next week it will be high with a probability of 0.9 and low with a probability of (ii) If volume is low this week then it will be high next week with a probability of 0.5. Assume that state 1 is high volume and that state 2 is low volume. (Note: Express your answers as decimal fractions rounded to 4 decimal places (if they have more than 4 decimal
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![If volume is high this week, then next week it will be high with a probability of 0.9 and low with a probability of 0.1.
If volume is low this week, then it will be high next week with a probability of 0.5.
Assume that **state 1 is high volume** and that **state 2 is low volume**.
*(Note: Express your answers as decimal fractions rounded to 4 decimal places (if they have more than 4 decimal places).)*
1. Find the transition matrix for this Markov process.
\[
P =
\begin{bmatrix}
\_\_\_\_ & \_\_\_\_ \\
\_\_\_\_ & \_\_\_\_ \\
\end{bmatrix}
\]
2. Find the four-step transition matrix \( P(4) \):
\[
P(4) =
\begin{bmatrix}
\_\_\_\_ & \_\_\_\_ \\
\_\_\_\_ & \_\_\_\_ \\
\end{bmatrix}
\]
3. If the volume is high this week, what is the probability that it will be high 4 weeks from now (use \( P(4) \))?
\[
\_\_\_\_
\]
4. If the volume is high this week, what is the probability that it will be low 4 weeks from now (use your answer to the preceding question to derive the answer to this question if you can)?
\[
\_\_\_\_
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F36a79c17-bf73-44c3-9503-d2f30f855206%2Fa3e5c11c-6ab2-4f3e-afbe-bc243a432172%2Fom43dsi_processed.png&w=3840&q=75)
Transcribed Image Text:If volume is high this week, then next week it will be high with a probability of 0.9 and low with a probability of 0.1.
If volume is low this week, then it will be high next week with a probability of 0.5.
Assume that **state 1 is high volume** and that **state 2 is low volume**.
*(Note: Express your answers as decimal fractions rounded to 4 decimal places (if they have more than 4 decimal places).)*
1. Find the transition matrix for this Markov process.
\[
P =
\begin{bmatrix}
\_\_\_\_ & \_\_\_\_ \\
\_\_\_\_ & \_\_\_\_ \\
\end{bmatrix}
\]
2. Find the four-step transition matrix \( P(4) \):
\[
P(4) =
\begin{bmatrix}
\_\_\_\_ & \_\_\_\_ \\
\_\_\_\_ & \_\_\_\_ \\
\end{bmatrix}
\]
3. If the volume is high this week, what is the probability that it will be high 4 weeks from now (use \( P(4) \))?
\[
\_\_\_\_
\]
4. If the volume is high this week, what is the probability that it will be low 4 weeks from now (use your answer to the preceding question to derive the answer to this question if you can)?
\[
\_\_\_\_
\]
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