Markov process using transitional probability matrix(tpm) | Long run | Part-3 | Mathspedia |

TL;DR

This video discusses a Markov process problem involving a company executive who changes car brands each year, and the probabilities of transitioning between different car brands.

Transcript

this video will take up one more problem based on markov process dpm okay transistor probability matrix the question is uh company executive changes his car every year if he has a car of brand a okay brand a he changes over to a car of brand b different brands are there okay if he has a car of brand b then he changes over to a car of brand c howeve... Read More

Key Insights

• 😨 The Markov process problem discussed in the video involves a company executive changing car brands annually based on a specific transition pattern.
• 😨 The Transistor Probability Matrix (TPM) is crucial for calculating the probabilities of transitioning between different car brands in the future.
• 😨 Matrix multiplication is used to find the probabilities of having specific car brands in certain years.

Questions & Answers

Q: What is the purpose of using the Transistor Probability Matrix (TPM) in the context of this problem?

The TPM is used to represent and calculate the probabilities of transitioning between different car brands based on the given transition pattern. It allows us to find the probabilities of having specific car brands in the future.

Q: How is the TPM calculated for the given problem?

The TPM is a 3x3 matrix where each element represents the probability of transitioning from one car brand to another. The probabilities are determined based on the given brand transition pattern and the assumption that the executive is equally likely to choose any car brand if he has a car of brand C.

Q: How are the probabilities of having specific car brands in certain years calculated?

To calculate the probabilities, we use the concept of matrix multiplication. By raising the TPM to different powers, we can find the probabilities of having specific car brands in different years. The initial state is represented by A^0, and the desired year is determined by the power to which the TPM is raised.

Q: What is the probability of having a car of brand A in 2010 and brand B in 2011?

The probability of having a car of brand A in 2010 is found by multiplying the initial state A^0 with the TPM raised to the power of 2 (A^2). The probability of having a car of brand B in 2011 is found by multiplying the initial state A^0 with the TPM raised to the power of 3 (A^3).

Key Insights:

• The Markov process problem discussed in the video involves a company executive changing car brands annually based on a specific transition pattern.
• The Transistor Probability Matrix (TPM) is crucial for calculating the probabilities of transitioning between different car brands in the future.
• Matrix multiplication is used to find the probabilities of having specific car brands in certain years.
• The probabilities are influenced by the initial state, the brand transition pattern, and the assumptions regarding the decision-making process of the executive.

Summary & Key Takeaways

• The video introduces a problem where a company executive changes his car brand annually, following a specific brand transition pattern.

• The video explains the concept of the Transistor Probability Matrix (TPM) and how it represents the probabilities of transitioning between different car brands.

• The video provides step-by-step calculations to find the probabilities of having a specific car brand in certain years based on the given TPM.