Because of the proliferation of more affordable automated office equipment, more and more companies are turning to them as replacements for obsolete equipment. The following transition matrix describes the Markov process. Here, stands for electric typewriters, stands for electric typewriters with some form of word processing capabilities, and stands for computers with word processing software. E W C
Rewrite it so that the absorbing state appears first. Partition the resulting matrix and identify the submatrices and .

Question

Because of the proliferation of more affordable automated office equipment, more and more companies are turning to them as replacements for obsolete equipment. The following transition matrix describes the Markov process. Here,  stands for electric typewriters,  stands for electric typewriters with some form of word processing capabilities, and  stands for computers with word processing software. E W C  ​
Rewrite it so that the absorbing state appears first. Partition the resulting matrix and identify the submatrices  and  .
​

Quizplus · Accepted Answer

To rewrite the transition matrix with the absorbing state appears first, we need to rearrange the rows and columns. We want the absorbing state of "computers with word processing software" to appear first, followed by the other two states. Therefore, we rearrange the rows and columns as follows:

C E W
11eab448_e7a0_a009_acdb_51e22caa081a_TB6027_11 C1 E1 W1
11eab448_e7a0_78f7_acdb_b76e96e8d55c_TB6027_11 C2 E2 W2
11eab448_e7a0_78f6_acdb_cfb7505a1e25_TB6027_11 C3 E3 W3

Now, we can partition the matrix into two submatrices. The submatrix for the absorbing state consists of just the first row and column:

C1

The submatrix for the transient states consists of the last two rows and columns:

E2 W2
E3 W3

This gives us the following transition probability matrix:

C1 E2 W2 E3 W3
C1 1 0 0 0 0
E2 P11 P12 0 0
W2 P21 P22 0 0
E3 P31 P32 0 0
W3 P41 P42 0 0

Where P11, P12, P21, P22, P31, P32, P41, and P42 are the probabilities of transitioning between the transient states.

Therefore, the correct answer is D) 11eab448_e7a0_c71f_acdb_3f28963766d9_TB6027_11.

Because of the Proliferation of More Affordable Automated Office Equipment