Mock Exam 2 (Paper A)

[amcyp13]

Hi

Regarding question 2 of Mock exam 2 (Paper A), may I kindly ask how do we derive the matrix? what is the rational behind it?

Thank you in advance,
AM

 

[Andrew Martin]

Hello

As the change depends on the last two values, to formulate as a MC we use states representing pairs of changes instead of individual changes.

So we have states:

UU
UD
DU
DD

Now let's think about transitions between the states. If we are currently on UU then the next change is either U or D. Ie the set of three most recent changes is:

UUU; or
UUD

In the first case the most recent two changes are both UU so in terms of our MC, this is a transitions from UU to UU. In the second case, the most recent two changes are UD, so in terms of our MC, this is a transition from UU to UD. As P(U given last two were UU) is 0.2, we have P(UU -> UU) = 0.2 and P(UU -> UD) = 0.8. We also have P(UU -> DD) = 0 and P(UU -> DU) = 0 as this can't happen. This gives the first row the matrix and the others can be calculated similarly.

Hope this helps

Andy