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#451
Yesterday, 07:06 PM
 Jim Daniel Member SOA Join Date: Jan 2002 Location: Davis, CA College: Wabash College B.A. 1962, Stanford Ph.D. 1965 Posts: 2,558

Quote:
 Originally Posted by PerpetualMotion Can someone ELI5 the differences in these variances from Fall 2014 (ii) Drug A will be given to 1000 subjects comprising Cohort A. • With probability 80%, each subject in Cohort A will have q = 0.20 . • With probability 20%, each subject in Cohort A will have q = 0.05 . • Conditional on q, the lives have independent future lifetimes. ** I understand that everyone in the group will experience whichever q is chosen so we use (un?)conditional variance formula. I don't really know why this is though. (iii) Drug B will be given to 1000 subjects with independent future lifetimes, comprising Cohort B. The drug will affect different subjects differently and independently. • With probability 80%, any given subject in Cohort B will have q = 0.20 . • With probability 20%, any given subject in Cohort B will have q = 0.05 . ** This one you end up finding E(Q) and conditional variance of Q because any given subject can experience different Qs. I really just don't understand this topic, so if anyone can break it down I'd really appreciate it. Or if someone can point me to TIA videos or other online resources. This is a major flaw in my understanding of variance and I'm really trying to understand.
ii) says there is an 80% probability that you have 1000 trials with q = 0.2 [so a Binomial RV with m=1000 and q = 0.2] and a 20% probability that you have 1000 trials with q = 0.05 [so a Binomial RV with m=1000 and q = 0.05]. Thus the distribution is an 80/20 mixture of these two Binomial RV's. Get the mean and second moment by mixing and then get the variance. [My website has a free study note on mixture distributions.]

iii) says that each individual has an independent 80% probability of its q being 0.2 and a 20% probability of its q being 0.05. Thus, by mixing, each individual has a probability 0.8 (0.2) + (0.2) (0.05) =0.17 of death, and there are 1000 such individuals, so the number of deaths is Binomial with parameters 1000 and 0.17. So the mean and variance just come from this Binomial.
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#452
Yesterday, 07:15 PM
 PerpetualMotion Member SOA Join Date: Jan 2013 Location: Kentucky(Louisville) Studying for Exam MLC College: University of Louisville Alumni Favorite beer: Zombie Dust Posts: 325

Wow, that actually makes perfect sense. I'm going to check out that study note. I really appreciate it, I just know there's going to be a question like this on the exam
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And NUH is the letter I use to spell Nutches
Who live in small caves, known as Nitches, for hutches,
These Nutches have troubles, the biggest of which is
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#453
Yesterday, 07:37 PM
 Steveo1794 Member SOA Join Date: May 2016 Location: Ohio Studying for MLC College: Miami University (OH) Favorite beer: Anything Posts: 32

Quote:
 Originally Posted by PerpetualMotion Wow, that actually makes perfect sense. I'm going to check out that study note. I really appreciate it, I just know there's going to be a question like this on the exam
Did this question last night... Confused the hell out of me but once I really thought about it, it made sense.

I think about it like this:
The scenario in b(ii) has five total groups of 1000 each. In four of those five groups, everyone has q=.20. In the other one, everyone has q=.05.
The scenario in b(iii) is one group of 1000. 80% of the 1000 have q=.20 and the other 20% has q=.05.

Hope this helps.

---

Side note - Are we allowed to use pens on the written answer? Obviously not on the MC, but the WA?

Last edited by Steveo1794; Yesterday at 07:40 PM..
#454
Yesterday, 07:42 PM
 Jim Daniel Member SOA Join Date: Jan 2002 Location: Davis, CA College: Wabash College B.A. 1962, Stanford Ph.D. 1965 Posts: 2,558

Both of Steveo1794's interpretations are incorrect.
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#455
Yesterday, 08:21 PM
 Steveo1794 Member SOA Join Date: May 2016 Location: Ohio Studying for MLC College: Miami University (OH) Favorite beer: Anything Posts: 32

I wasn't referring to the literal scenarios presented in the problem, I was referring to how to distinguish between the "each subject will have" and "any given subject". That phrasing confused me, and thinking about it like that helps me.

Does the below explanation make sense? If not, please correct it.

Scenario b(ii) is 80% chance that 100% of the cohort will have q=.20 and a 20% chance that 100% of the cohort will have q=.05.
Scenario b(iii) is simply an 80% chance of a member of the cohort having q=.20 and a 20% chance of someone in the same cohort having q=.05.
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#456
Yesterday, 08:45 PM
 Jim Daniel Member SOA Join Date: Jan 2002 Location: Davis, CA College: Wabash College B.A. 1962, Stanford Ph.D. 1965 Posts: 2,558

Quote:
 Originally Posted by Steveo1794 I wasn't referring to the literal scenarios presented in the problem, I was referring to how to distinguish between the "each subject will have" and "any given subject". That phrasing confused me, and thinking about it like that helps me. Does the below explanation make sense? If not, please correct it. Scenario b(ii) is 80% chance that 100% of the cohort will have q=.20 and a 20% chance that 100% of the cohort will have q=.05. Scenario b(iii) is simply an 80% chance of a member of the cohort having q=.20 and a 20% chance of someone in the same cohort having q=.05.
My problem with how you described it is the following: correct solutions based on the statements you gave yield incorrect answers for both cases. However, you may have interpreted your statements in an incorrect way that produced correct answers in boith cases. It's good to be lucky.

Your explanation of b(ii) is correct.

Your explanation of b(iii) may be correct, but the wording strikes me as a little confusing. It would be clearer to say: For each member of the cohort, there is an 80% chance that that member's q is 0.2 and a 20% chance that that member's q is 0.05, and the results are independent from member to member.

By the way, I agree that the exam problem as stated is poorly worded, with the "any given subject" and "each subject" difficult to distinguish---and imagine what it's like for non-native English speakers! Of course, exam questions are often poorly worded, and it's not all that rare for them to use textbook terms to mean something different from their meaning in the textbook, or to be missing data, or for the wrong answer to be considered correct. Quality control truly sucks. Candidates need to be robust problem solvers in that the first part of the problem is to figure out what the problem really is.
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#457
Yesterday, 09:44 PM
 MySpaceTom SOA Join Date: Oct 2016 Posts: 7

The Written Answer instructions at the beginning of the exam state " Do not write answers to more than one question per sheet".

Does this mean every part (a, b, and c) to question 1, must be on an individual sheet? Or, is it okay to answer parts a, b, and c all on the same sheet?
#458
Yesterday, 10:38 PM
 PerpetualMotion Member SOA Join Date: Jan 2013 Location: Kentucky(Louisville) Studying for Exam MLC College: University of Louisville Alumni Favorite beer: Zombie Dust Posts: 325

Quote:
 Originally Posted by Jim Daniel By the way, I agree that the exam problem as stated is poorly worded, with the "any given subject" and "each subject" difficult to distinguish---and imagine what it's like for non-native English speakers! Of course, exam questions are often poorly worded, and it's not all that rare for them to use textbook terms to mean something different from their meaning in the textbook, or to be missing data, or for the wrong answer to be considered correct. Quality control truly sucks. Candidates need to be robust problem solvers in that the first part of the problem is to figure out what the problem really is.
I'm the first to admit that life isn't fair but that really seems like bs from the soa standpoint. We put in hundreds of hours worth of work for each of these exams, they should be held to a higher standard. Some problems are unnecessarily complex and it just doesn't feel right. The further I progress, the more it all seems like a cash grab. I hope when I'm an FSA I get to write problems that actually tests relevant knowledge. Until then.
__________________
P,FM MFE , C, MLC
Modules 1-8 IA
FA

And NUH is the letter I use to spell Nutches
Who live in small caves, known as Nitches, for hutches,
These Nutches have troubles, the biggest of which is
the fact there are many more Nutches than Nitches.
#459
Today, 12:10 AM
 NoFunnyStuff Member SOA Join Date: Jul 2009 Location: Green Bay, WI Studying for MLC College: Georgia State University Alumni Posts: 164

Quote:
 Originally Posted by noonelikesmodules Doing a profit/gain question. Specifies surrender and mortality RATES. Doesn't specify about timing of surrenders. Do we always assume EoY surrenders?
Most of the time yes, because if you have already paid for your insurance in BOY you would not surrender before the end of the year for something you have already paid for.
Hope that this help.
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