Actuarial Outpost ASM 3L 10th ed Practice Exam 4 #3
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 CAS 3 - specific material Please keep posts regarding material common to both exams in the upper forum

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#1
10-15-2011, 01:39 AM
 Doc Holiday Member Join Date: Aug 2006 Location: Tombstone Favorite beer: Anything that defiles myself Posts: 998
ASM 3L 10th ed Practice Exam 4 #3

Q: Prob of milk carton on the shelf is purchased on any day is 20%.
Milk cartons are discarded after 7 days.

Determine the avg number of full days a purchased milk carton is on the shelf.

[ (sum from 1 to 7 of .8^k) - 7(.8^.7) ] / (1-0.8^7)

I went with summing (1)(.8)(.2) + 2(.8^2)(.2) + ....
not sure why my answer didn't turn out.
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#2
10-15-2011, 07:34 AM
 Gandalf Site Supporter Site Supporter SOA Join Date: Nov 2001 Location: Middle Earth Posts: 26,452

There are threads on this. You might find them by searching for "carton" or "cartons" [maybe in MLC instead of 3L]. The key is that it is asking about a purchased milk carton. That makes it conditional upon the milk carton having been purchased.

The numerator is just the "Darth Vader" rule (survival function method) way of calculating the expected number of days. The last term removes the 7 days for any that weren't purchase. Your density method approach should give the same thing.

The (1-0.8^7) as the denominator is for the conditional nature: remove those not purchased from consideration.

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