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#242




I've made my first pass at Venter and Clark now (still just watching TIA videos, not doing problems), and I have to say this material seems way more intuitive and easier than exam 8 did on my first pass so far. Definitely still feeling there's more memorization of formulas though.
Still on pace to finish up all the TIA videos by late January around 3 months out and then I'm gonna start on a second pass of the material with diving into problems in each section as I go through. 
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Part 2) calculates the age of the average accident date for the earned period. For AYs, this is straightforward: If the AY isn't fully earned yet, then t months of it have been earned and t/2 is the age of the average accident date. If the AY has been fully earned, then the average accident date is at 6 months. The age of the average accident date is then just t  6 months. For PYs: If t is greater than 24 months, then the Expos(t) = 1 so Clark's formula just reduces to t12. This makes sense because if we're over 24 months from the beginning of the policy year, the entire policy year has earned out and the average accident date will be 12 months from the beginning of it. For t less than 12 months and t in 1224 months, this is tricky. Let's start with t < 12: We want to find the age of the average accident date for a PY t months into it. We can do this by setting up an integral. I did this on paper and didn't take a picture, so it might be hard to follow (I can upload a pic if you think it'll help). For a policy written x months into the policy year, the age of its average accident date is (tx)/2. This is because the policy has been in effect for tx months and at month t the average accident date is x + (tx)/2. So the age of the average accident date for this policy is t [x + (tx)/2] = (tx)/2. This is what we want to integrate across our triangle. However we have to weight this by the portion of the area that consists of policies written at x. If we take a sliver of width dx of our triangle, then the portion of the total area in this sliver is dx*(tx)/(0.5*t^2). Therefore, we have to integrate this quantity times (tx)/2 from 0 to t to get the age of the average accident date as of t months. This gives us t/3. I don't feel like working out t between 12 and 24, but you could do it in a similar way. Honestly though, I wouldn't focus on stuff like this in studying for the exam. I'd say there's essentially a zero percent chance you'll need to know this or the PY formulas. Last edited by amp019372; 12312019 at 08:23 PM.. 
#247




Here's an upload of my picture for setting up the integral.
Spoiler: The weight dx*(tx)/(0.5t^2) is the portion of that triangle's area that is in the sliver of width dx. Edit: Sorry the picture size is so large. Last edited by amp019372; 01012020 at 08:49 AM.. 
#249




I get 120 hours per exam sitting. I usually use 1 hour a day for a few months leading up to the exam, then ramp up to 2 hours a day when it gets closer. And I take off around 3 full days right before the exam. 5 days seems really low.

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