**Markov Process and Transition Matrix**The text describes a problem involving a Markov process with the following rules:- If the volume is high this week, it will be high next week with a probability of 0.6 and low with a probability of 0.4.- If the volume is low this week, it will be high next week with a probability of 0.2.**State Definitions:**- State 1: High Volume- State 2: Low Volume**Tasks:**1. **Find the Transition Matrix for this Markov Process:** The transition matrix \( P \) is represented as: \[ P = \begin{bmatrix} \, & \, \\ \, & \, \\ \end{bmatrix} \] This matrix will have probabilities for transitioning between states: from high to high, high to low, low to high, and low to low.2. **Calculate Probabilities:** (2) If the volume this week is high, what is the probability that the volume will be high two weeks from now? [Empty box for calculation] (3) What is the probability that volume will be high for three consecutive weeks? [Empty box for calculation] This educational content focuses on understanding and applying the concept of a transition matrix in a Markov process and calculating the resulting state probabilities.

Assume that state 1 is high volume and state 2 is low volume. 1) Given that, if the volume is high this week then next week it will be high with probability of 0.6 and low with probability of 0.4. Also, if the volume is low this week then next week it will be high with probability of 0.2 Hence, the volume is low this week then next week it will be low with probability of 0.8. Therefore, the transition matrix is given by, P=0.60.40.20.8 2) Now, we have to find if the volume is high this week then the probability that the volume will be high two weeks from now. P2=0.60.40.20.8×0.60.40.20.8P2=0.440.560.280.72 Hence, if the volume is high this week then the probability that the volume will be high two weeks from now is 0.44. 3) Now, we have to find the probability that the volume will be high for three consecutive weeks. P3=P2×PP3=0.440.560.280.72×0.60.40.20.8P3=0.3760.6240.3120.688 Hence, the probability that the volume will be high for three consecutive weeks is 0.376.

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(1) If volume is high this week, then next week it will be high with a probability of 0.6 and low with a probability of 0.4. (ii) If volume is low this week then it will be high next week with a probability of 0.2. Assume that state 1 is high volume and that state 2 is low volume. (1) Find the transition matrix for this Markov process. P = --- (2) If the volume this week is high, what is the probability that the volume will be high two weeks from now? What is the probability that volume will be high for three consecutive weeks?

(1) If volume is high this week, then next week it will be high with a probability of 0.6 and low with a probability of 0.4. (ii) If volume is low this week then it will be high next week with a probability of 0.2. Assume that state 1 is high volume and that state 2 is low volume. (1) Find the transition matrix for this Markov process. P = --- (2) If the volume this week is high, what is the probability that the volume will be high two weeks from now? What is the probability that volume will be high for three consecutive weeks?

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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(i) 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. (ii) If volume is low this week then it will be high next week with a probability of 0.2. Assume that state 1 is high volume and that state 2 is low volume. (1) Find the transition matrix for this Markov process. ... P = ... ... ... (2) If the volume this week is high, what is the probability that the volume will be high two weeks from now? (3) What is the probability that volume will be high for three consecutive weeks? ...
(i) If volume is high this week, then next week it will be high with a probability of 0.6 and low with a probability of 0.4. (ii) If volume is low this week then it will be high next week with a probability of 0.1. Assume that state 1 is high volume and that state 2 is low volume (1) Find the transition matrix for this Markov process. (2) If the volume this week is high, what is the probability that the volume will be high two weeks from now? (3) What is the probability that volume will be high for three consecutive weeks?
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