Question

a) Each production schedule is classified as low, medium, or high. During any given year, 5% of all high schedule can be moveto l and 15% move to a medium schedule; also, 3% of all low schedule can be move to high schedule, and 8% move to medium schedule: finally 6% of all medium can be move to high schedule, and 10% can move to a low schedule b) ow schedule 1/4 0 2 1/4 1/2 1/3 1/3

For each problem construct a Markov Matrix with procedure.
Step by step

Answer 1

(a)

As per the problem statement,

High to Low: 5%
High to Medium: 15%
So, High to High: 100% - (15%+5%) = 80%

From \ To	High	Medium	Low
High	0.80	0.15	0.05

Low to High: 3%
Low to Medium: 8%
So, Low to Low: 100% - (3%+8%) = 89%

From \ To	High	Medium	Low
Low	0.03	0.08	0.89

Medium to High: 6%
Medium to Low: 10%
So, Medium to Medium: 100% - (6%+10%) = 84%

From \ To	High	Medium	Low
Medium	0.06	0.84	0.10

Combining the three entries in a single matrix, the Markov single-step transition matrix is as follows:

0.80	0.15	0.05
0.06	0.84	0.10
0.03	0.08	0.89

b)

As per the network diagram:

From state '0'

1/2 has gone to state '0'
1/4 has gone to state '1'
1/4 has gone to state '2'

From \ To	0	1	2	3
0	1/2	1/4	1/4	0

From state '1'

'1' has gone to state '2'

From \ To	0	1	2	3
1	0	0	1	0

From state '2'

1/3 has gone to state '0'
1/3 has gone to state '2'
1/3 has gone to state '3'

From \ To	0	1	2	3
2	1/3	0	1/3	1/3

From state '3'

1 has gone to state '3'

From \ To	0	1	2	3
3	0	0	0	1

Combining the above three entries in one matrix, we get the single-step transition matrix as follows:

1/2	1/4	1/4	0
0	0	1	0
1/3	0	1/3	1/3
0	0	0	1