Question

Suppose that the probability of a dry day (State 0) following a rainy day (State 1) is 1/3 and the probability of a rainy day following a dry day is 1/2. Write the transition probability matrix of the above Markov chain. 

Given that 1st May is a dry day, then calculate

i) the probability that 3rd May is also a dry day.

ii) the stationary probabilities.

06 Feb 2024
Answer :
Word Count : 566

To construct the transition probability matrix \( P \) for the Markov chain with states representing dry (State 0) and rainy (State 1) days, we use the given transition probabilities:

\[
P = \begin{pmatrix}
P_{00} & P_{01} \\
P_{10} & P_{11}
\end{pmatrix}
\]

Where:
- \( P_{00} \) is the probability of transitioning from a dry day to another dry day.
- \( P_{01} \) is the probability of transitioning from a dry day to a rainy day.
- \( P_{10} \) is the probability of transitioning from a rainy day to a dry day.
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