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Long-Term Actuarial Math Old Exam MLC Forum

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  #1  
Old 07-02-2019, 03:50 PM
Pro-Procrastinator Pro-Procrastinator is offline
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Default ASM 1st edition 4th Printing Q10.2

Why is the solution essentially calculating 1q79.5 as opposed to 0.5|1q79 = .5p79 * 1q79.5, which takes into consideration the probability of survival to age 79.5?

What is the difference between this question and 10.7, which to me is the same type of question but the latter concept is used instead of the former?

Note: I understand the math being done, I just don't understand why it's 1q79.5 as opposed to 0.5|1q79 in 10.2.
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  #2  
Old 07-02-2019, 04:22 PM
Seasplash Seasplash is offline
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Could you post the problem for us to see? Thanks.
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Old 07-02-2019, 07:12 PM
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see attachment for 10.2 and 10.7
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File Type: pdf 10-2 02-Jul-2019 18-39-14.pdf (1.05 MB, 23 views)
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Old 07-02-2019, 07:32 PM
Colymbosathon ecplecticos's Avatar
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Calendar year 2025 is one year long, starting 1/1/2025 and ending 12/31/2025, and you are given survival to 1/1/2025.
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Old 07-03-2019, 08:27 AM
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Quote:
Originally Posted by Colymbosathon ecplecticos View Post
Calendar year 2025 is one year long, starting 1/1/2025 and ending 12/31/2025, and you are given survival to 1/1/2025.
Why is it 1q79.5 as opposed to 0.5|1q79 = .5p79 * 1q79.5? What's the difference between Q10.2 and Q10.7?
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Old 07-03-2019, 08:35 AM
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Colymbosathon ecplecticos Colymbosathon ecplecticos is offline
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Quote:
Originally Posted by Pro-Procrastinator View Post
Why is it 1q79.5 as opposed to 0.5|1q79 = .5p79 * 1q79.5?
You are given that he is alive on 1/1/2025 --- he is age 79.5 on 1/1/2025.
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Old 07-03-2019, 08:40 AM
Abraham Weishaus Abraham Weishaus is offline
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Quote:
Originally Posted by Pro-Procrastinator View Post
Why is the solution essentially calculating 1q79.5 as opposed to 0.5|1q79 = .5p79 * 1q79.5, which takes into consideration the probability of survival to age 79.5?

What is the difference between this question and 10.7, which to me is the same type of question but the latter concept is used instead of the former?

Note: I understand the math being done, I just don't understand why it's 1q79.5 as opposed to 0.5|1q79 in 10.2.
You must distinguish between joint probability and conditional probability. Recall from probability the formula
Q 10.2 is asking for a conditional probability: probability of dying between times 0.5 and 1.5 GIVEN survival to time 0.5. By the formula just cited, that is the same as the probability of surviving 0.5 years and dying in 1 year divided by the probability of surviving 0.5 years.

Q 10.7 is asking for a joint probability: probability of surviving 2 years and dying in the third year. That is the numerator only of Q 10.2.
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Old 07-03-2019, 11:11 AM
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Quote:
Originally Posted by Abraham Weishaus View Post
You must distinguish between joint probability and conditional probability. Recall from probability the formula
Q 10.2 is asking for a conditional probability: probability of dying between times 0.5 and 1.5 GIVEN survival to time 0.5. By the formula just cited, that is the same as the probability of surviving 0.5 years and dying in 1 year divided by the probability of surviving 0.5 years.

Q 10.7 is asking for a joint probability: probability of surviving 2 years and dying in the third year. That is the numerator only of Q 10.2.
Right. Thanks. And I just realized even if I used 0.5|1q79 = .5p79 * 1q79.5, the probability of surviving 0.5 years would be 1 in this case
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