CT4(103) - Sept 2006

[avanbuiten]

im starting to think my answer was wrong now

i simply put in 3 states (0,1,2) as i thought this solved all cases. If you are in 0, you had to come from 1 or be in 0 already, so therefore you couldnt have claimed in last 2yrs. If in 1 you had to come from 0 (i.e 1 claim in last 2yrs) or from 2 (1 claim and 1 no claim). If you are in 2 you had to come from 1 or already be in 2.
Does this work?

Unfortunately it doesn't work!

Your middle state fails the definition of the Markov property; "the probability of being in a future state depends only on the current state occupied". Remember we are working in one year intervals and not 2-year intervals.

So the states are:

S0: Starting state with no claims. If you don't claim, you stay.
S1: You arrive here from S0 if you claim in previous year.
S2: You arrive here from S1 if you claim in previous year. If you claim again, you stay.
S1-: You arrive here from S2 if you have a claim-free year. Alternatively, arrive from S1 if you don't claim. Then if you claim, go to S1. If you don't claim go to S0.

So the states are set up now based on one-year cycles and one-year histories - which is necessary to satisfy Markov definition when working in single years.

In the attached image; C = Claim & N = No-claim.

Don't be too sad though, I bet you pick up a lot of marks for your working on the rest of the question.

And I could always be wrong of course.

..the pass mark for CT exams is 50-60 with an average of 55.

I was hoping it might be 48%.

Note to acted: If you like you can use my attached graph in your asset solutions next year It's quality!

 

[decrement]

u r right, i did it wrong

but i did carry on and answer the rest of the question. How many marks would u lose overall, because of the mistake of the states diagram? You must get some credit for saying why it converges to stationary distribution and calcuting the values surely?

 

[scarlets]

what about the survival function graph, did you use a pencil & ruler and graph paper? as I certainly didn't, I just sketched it quickly in the answer booklet and tried to label it. I didn't even bring a pencil and ruler with me to the exam and didn't have time to draw a neat graph, hope they won't deduct many marks for that. I never like graph questions because although I consider it easy marks it is time consuming and frankly they're testing a GCSE level skill so what's the point.

 

[avanbuiten]

u r right, i did it wrong

but i did carry on and answer the rest of the question. How many marks would u lose overall, because of the mistake of the states diagram? You must get some credit for saying why it converges to stationary distribution and calcuting the values surely?

They're not meant to penalise you twice - so theoretically you can get all the remaining marks.

I said it converges because the states are aperiodic - which was a guess as I didn't even know the states at that time (just applied reasoning).

 

[scarlets]

I think I got the states correct but only with a few minutes to spare since it took a lot of thinking time to come up with the correct states... this meant I had to rush to write down the transition matrix (possibility of a silly error) and I didn't have enough time to actually work out the stationary distribution but just wrote down pi*P=pi etc. without actually doing the calculations. Could I end up getting less marks than someone who put down incorrect states but did the rest of the question correct. I would feel a bit hard done by if this was the case.

I wonder what Acted's advice on exam technique would be here... is it best to spend 5-10 minutes thinking and nailing the state space or would time be better spent completing the rest of the question to get method marks?!?!

 

[Sauny Bean]

Managed to get this one on the fourth attempt in the last chance saloon before it doubled up. As it was my last CT, I'd already decided not to redo it next April and just leave it for the very end in the event I didn't get it. It helped having this strategy beforehand as it took the pressure off being so reliant on passing it.