Spring 2012 3L PAK

[spade]

Originally Posted by tfoster

I agree with you Fianchetto. If the question asked for the expected time to failure from decrement 2 instead of decrment 1 and following that logic you would get 0.8. Just doesn't make sense given the force of mortality is 25% of decrement 1.

Your link isn't working for me.

And yes, if you're given that the death is from decrement 1, then I agree the expected time until failure would be shorter than if you were given that the death is from decrement 2. However, you're not given anything. The writer of this question should not have used the notation E[T | J=1] because it suggests conditional expectation, but the written description does not suggest that.

If you can tell the difference between what the notation is asking for and what the wording is asking for, then it boils down to: which one did they really mean to ask? From historically discrepancies, my bet is that the wording reflects what the CAS intended to ask, and the notation was just poorly chosen, as it led to misinterpretations.

[tfoster]

Originally Posted by spade

Your link isn't working for me.

And yes, if you're given that the death is from decrement 1, then I agree the expected time until failure would be shorter than if you were given that the death is from decrement 2. However, you're not given anything. The writer of this question should not have used the notation E[T | J=1] because it suggests conditional expectation, but the written description does not suggest that.

If you can tell the difference between what the notation is asking for and what the wording is asking for, then it boils down to: which one did they really mean to ask? From historically discrepancies, my bet is that the wording reflects what the CAS intended to ask, and the notation was just poorly chosen, as it led to misinterpretations.

It's a pdf file. faculty.atu.edu/mfinan/actuarieshall/MLCbook2.pdf Page 643, Question 64.3

[spade]

Yes, I agree that that is how the conditional expectation should be calculated. But I'm suggesting that that's not what the CAS intended to ask for. Would you agree there is a difference between "E[T|j=1]" and "the expected time to failure from decrement 1"?

[Fianchetto]

If it were 3.2 that would put the other dec at .8 and that just doesn't make sense to me. I just don't see any interpretation that would make #6 have an answer of A. Just my take, and ultimately it just matters what CAS thinks.

[Colymbosathon ecplecticos]

Originally Posted by spade

Yes, I agree that that is how the conditional expectation should be calculated. But I'm suggesting that that's not what the CAS intended to ask for. Would you agree there is a difference between "E[T|j=1]" and "the expected time to failure from decrement 1"?

If you fail from some other decrement, how long did it take you to fail from decrement 1?

[Londondrug]

lol, I find this, looks like the taker didn't complain too much.