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
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
