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 Long-Term Actuarial Math Old Exam MLC Forum

#11
07-15-2009, 09:40 AM
 Bama Gambler James Washer / Notes Contributor SOA Join Date: Jan 2002 Location: B'ham, AL Posts: 17,239

Quote:
 Originally Posted by optimizer Did you mean to say that $f_{T(x)}(t)\ dt$ is the probability that a life aged $x$ dies between ages $x+t$ and $x+t+dt$ ?
Yes. I'll edit my post.
Quote:
 According to your definition, $f_{T(x)}(t)$ is a pdf.
$f_{T(x)}(t)$ is a pdf.
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#12
07-15-2009, 09:56 AM
 optimizer Member Join Date: Mar 2009 Studying for VEE & FAP Posts: 352

Quote:
 Originally Posted by Bama Gambler That's a lot to say every time so I find it more convenient to just that $f_{T(x)}(t) = {}_tp_x \mu(x+t)$ is the probability that a life age $x$ dies in exactly $t$ years... .
I think you also need to change this statement.
#13
07-15-2009, 10:00 AM
 Bama Gambler James Washer / Notes Contributor SOA Join Date: Jan 2002 Location: B'ham, AL Posts: 17,239

No I just say that b/c it is convenient. I know it isn't exactly correct, but it is a heck of lot easier and faster to say.
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#14
07-20-2009, 08:03 PM
 nhm0089 Member Join Date: Feb 2007 Posts: 41

i have a quick question. For a population which contains equal numbers of males and females at birth:

For males $\mu^{m}_{x} = 0.10, x>= 0$
For females $\mu^{f}_{x} = 0.08, x>= 0$

find q60. this is question 4.36 with asm. when solving the problem [IMG]http://www.actuarialoutpost.com/cgi-bin/mimetex.cgi?l_{60}^{m}\, =\, e^{-.1*60}=0.002478752[/IMG] was used in placed of tpx. Why. I am a little confused because above is tpx under constant force. how can lx be used. Can you explain.
#15
07-20-2009, 08:05 PM
 nhm0089 Member Join Date: Feb 2007 Posts: 41

sorry I tried to copy and past from the 4.36 thread, but if you can follow the tread under mlc maybe you will understand.
#16
07-20-2009, 09:42 PM
 Bama Gambler James Washer / Notes Contributor SOA Join Date: Jan 2002 Location: B'ham, AL Posts: 17,239

I'm sorry but I'm not clear on what you are asking. This is B.1 #169 in the TIA problem sets. There is a couple of ways you can work this problem. Here is one way:

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#17
07-20-2009, 11:07 PM
 nhm0089 Member Join Date: Feb 2007 Posts: 41

This is a simpler way to solve the problem than in the tread for asm 4.36.
I am still wondering, however, when the person solved the problem in the tread, they used under the constant force of mortality tpx for the male(constant force also applies to the females in this problem) is exp^(-.1 x 60) but instead of using the notation tpx they used lx(male) is exp^(-.1 * 60). I want to know why did they used lx instead of tpx. Are lx and tpx, the same thing is this problem.
#18
07-20-2009, 11:12 PM
 Bama Gambler James Washer / Notes Contributor SOA Join Date: Jan 2002 Location: B'ham, AL Posts: 17,239

Remember $l_0$ is arbitrary. This person set $l_0 = 1$. Then $l_x = l_0 \, {}_xp_0 = {}_xp_0$.
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#19
07-20-2009, 11:17 PM
 nhm0089 Member Join Date: Feb 2007 Posts: 41

sorry s(x) = e^(-ux) so are lx and s(x), the same thing, in this problem.
#20
07-20-2009, 11:25 PM
 nhm0089 Member Join Date: Feb 2007 Posts: 41

Thanks!!!!!!!!!!!!

 Tags the infinite actuary, tia