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 Short-Term Actuarial Math Old Exam C Forum

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#1
06-10-2018, 10:35 PM
 RockOn Member SOA Join Date: Dec 2013 Studying for Exam C Favorite beer: Polygamy Porter Posts: 83
SOA #28

Hello,
Can someone please advise me if I can use the following formula (instead of the simple integration) to answer SOA #28?

E[X^a] = (u^3 - d^3) / 3 (u - d)

Where u is the high end of each interval and d is the low end of each interval?

Thank you!
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#2
06-10-2018, 11:15 PM
 Academic Actuary Member Join Date: Sep 2009 Posts: 8,388

You would get a quicker response if you would post the question.
#3
06-11-2018, 12:35 AM
 Marcie Member CAS Join Date: Feb 2015 Posts: 9,574

Quote:
 Originally Posted by Academic Actuary You would get a quicker response if you would post the question.
#4
06-11-2018, 11:57 AM
 bravesandfalcons Member CAS SOA Join Date: Dec 2013 College: Georgia State University Posts: 261

Quote:
 Originally Posted by RockOn Hello, Can someone please advise me if I can use the following formula (instead of the simple integration) to answer SOA #28? E[X^a] = (u^3 - d^3) / 3 (u - d) Where u is the high end of each interval and d is the low end of each interval? Thank you!
Going by the formula you just gave, E[X^2] = E[X^3] = E[X^4].

Did you mean to perhaps substitute the 3's on the right hand side with a's?
#5
06-11-2018, 12:01 PM
 bravesandfalcons Member CAS SOA Join Date: Dec 2013 College: Georgia State University Posts: 261

Quote:
 Originally Posted by Academic Actuary You would get a quicker response if you would post the question.
Quote:
 Originally Posted by Marcie
Couldn't get the picture to post. Hopefully, the attachment is there.

Looks like that worked!
Attached Images

#6
06-11-2018, 12:26 PM
 ARodOmaha Member SOA Join Date: May 2016 Location: Omaha, NE Studying for MFE College: University of Nebraska (alma mater) Favorite beer: Captain Morgan Posts: 188

Quote:
 Originally Posted by bravesandfalcons Couldn't get the picture to post. Hopefully, the attachment is there. Looks like that worked!
Yes, the correct approach is to use E[X^2] = (b^3 - a^3) / (3(b-a)) for each interval. For the limited expected value piece, first rewrite the intervals with a maximum value of 150. Just be sure to weight the intervals by their empirical probabilities.
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#7
06-11-2018, 01:41 PM
 Academic Actuary Member Join Date: Sep 2009 Posts: 8,388

Your formula gives a conditional expectation: E[X^2| d < X < u]
#8
06-12-2018, 02:49 PM
 RockOn Member SOA Join Date: Dec 2013 Studying for Exam C Favorite beer: Polygamy Porter Posts: 83

Quote:
 Originally Posted by ARodOmaha Yes, the correct approach is to use E[X^2] = (b^3 - a^3) / (3(b-a)) for each interval. For the limited expected value piece, first rewrite the intervals with a maximum value of 150. Just be sure to weight the intervals by their empirical probabilities.
Hi ARodOmaha,
Thank you for the response. I did try that but could not seem to get the right answer. For the last part of the interval above 150 would it be: [3 * (150^2)]/78?

Thank you!
__________________
EXAMS: P | FM | MFE | MLC | STAM | PA |
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#9
06-12-2018, 02:50 PM
 RockOn Member SOA Join Date: Dec 2013 Studying for Exam C Favorite beer: Polygamy Porter Posts: 83

Quote:
 Originally Posted by bravesandfalcons Couldn't get the picture to post. Hopefully, the attachment is there. Looks like that worked!
Thank you for posting the question, bravesandFalcons!
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EXAMS: P | FM | MFE | MLC | STAM | PA |
VEE: ECON | STATS | CORP FINANCE |
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#10
06-12-2018, 03:44 PM
 ARodOmaha Member SOA Join Date: May 2016 Location: Omaha, NE Studying for MFE College: University of Nebraska (alma mater) Favorite beer: Captain Morgan Posts: 188

Quote:
 Originally Posted by RockOn Hi ARodOmaha, Thank you for the response. I did try that but could not seem to get the right answer. For the last part of the interval above 150 would it be: [3 * (150^2)]/78? Thank you!
Yes, the last part is a little different because you are essentially going from 150 to 150. So it is E[X^2] = 150^2. Or think of E[X^2] as Var(X) + E[X]^2. The variance of 150 here is 0. The expected value is 150^2. Weight this with 3/74.
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