A2016 Q 10

[Nimisha]

Hi
In question 10 of CT4 part 4 ,I made the transition matrix by first adding the rows for company A and D and then the columns.
So my ans is different than the one given as in the solution first the columns are added for A and D and then the rows.

Please confirm if my method is correct or not.

 

[Andrew Martin]

Hello

You need to add the columns rather than the rows.

It is perhaps easier to consider first companies B and C. The new probabilities we need are:

B -> A or D
C -> A or D

These probabilities are the sums of the respective columns for A and D. Ie:

P(B -> A or D) = 0.2 + 0.1 = 0.3
P(C -> A or D) = 0.3 + 0.1 = 0.4

Similarly, think about companies A and D:

P(A -> A or D) = 0.5 + 0.1 = 0.6
P(D -> A or D) = 0 + 0.6 = 0.6

Combining the columns gives:

Addda B C
A 0.6 0.2 0.2
B 0.3 0.6 0.1
C 0.4 0.2 0.4
D 0.6 0.2 0.2

We now need to combine the first and last row to give a single entry for Addda. The rows for A and D are the same so we simply have:

Addda B C
Addda 0.6 0.2 0.2
B 0.3 0.6 0.1
C 0.4 0.2 0.4

If the rows were different then we need more information to calculate blended transition probabilities out of the new combined state.

Hope this helps

Andy