in example 5.1 in the quick approach used to calculate the probability of going from state 0 to state 2 in 3 time steps (NCD model) there is a section in the notes which says "..since we know that the distribution at time is (1,0,0) we can calculate the probability distribution.." I'm not entirely sure what that distribution means, does it mean we know we will always start in state 0 and not in state 1 and state 2? Thanks

I used NTU's CT4 notes, so I won't have seen the Acted notes yet. However, I believe that the context of the question will mention in some way what the starting distribution, if any, is. For instance, in the NCD model, a new customer at time 0 will usually only start in state 0. Then they can transition to the other states as time pass.

in that particular example, it wanted to calculate the probability of being at the max discount after 3 years given that we do not qualify for any discount initially, hence (1,0,0) was used as the start for this case. It means that we are already at state 0 at the beginning of the time period.