The S1 and S2, if
Answer to Problem 1RE
The S1 matrix is
The S2 matrix is
Explanation of Solution
The initial state matrix S0 and the transition matrix P is given below:
If P is the transition matrix and S0 is an initial-state matrix for a Markov chain, then the kth-state matrix is given by
The entry in the ith row and jth column of
The sum of the entries in each row of
Therefore,
In order to multiply matrices,
Make sure that the number of columns in the first matrix equals the number of rows in the second matrix.
Multiply the elements of each row of the first matrix by the elements of each column in the second matrix.
Hence, the S1 matrix is
This matrix gives us the probabilities of a randomly chosen person being in state A or B on the first trial after the start of the value.
Now see that the A's value has increased from 30% to 32 %.
Now calculate
Calculate the
Therefore,
Hence, the S2 matrix is
This matrix gives us the probabilities of a randomly chosen person being in state A or B on the second trial after the start of the value.
Now see that the A's value has increased from 30% to 32.80 %.
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Chapter 15 Solutions
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