Actuarial Outpost SOA 3 Nov 2003 Questions
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#11
11-04-2003, 07:16 PM
 Msta Member Join Date: Nov 2002 Posts: 53

The one with the LER? I got .2.

E(X^x) = .2
E(X) = 1
#12
11-04-2003, 07:18 PM
 sleg Member Join Date: May 2002 Posts: 118

Quote:
 Originally Posted by Msta The one with the LER? I got .2. E(X^x) = .2 E(X) = 1
Yeah, wasnt it just the area under and to the left of 20? .01*20 for the LEV
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#13
11-04-2003, 07:19 PM
 taaveez Join Date: May 2003 Posts: 28

I just maade a blip somewhere in the calculations that I couldnt fix.

There was this annoying feature of the questions on this exam that if you made an error you would almost never be able to spot it unless at the expense of a couple other problems.
#14
11-04-2003, 07:21 PM
 TenaciousMV Member SOA AAA Join Date: Nov 2002 Posts: 341

I agree that (X^x)=20, but E(x) isn't 100... it's more like 55-60.

#15
11-04-2003, 07:24 PM
 Msta Member Join Date: Nov 2002 Posts: 53

E(X) was .01 up to 80, then grade to 0 by 120.

80*.01 = .8
.01*(40)/2 = .2

E(X) = 1

and E(X^x) = .01*20 = .2 not 20
#16
11-04-2003, 07:26 PM
 taaveez Join Date: May 2003 Posts: 28

Unfortunately, my error was somewhere in the calculation of E(X) so although I got the right E(X^d), my E(X) was wrong.

How about the one with a benefit level to be chosen to minimize the variance on a policy? I think I got something 150K for that one.
#17
11-04-2003, 07:29 PM
 Rhizome Member Non-Actuary Join Date: Nov 2001 Posts: 1,875

Quote:
 Originally Posted by taaveez How about the one with a benefit level to be chosen to minimize the variance on a policy? I think I got something 150K for that one.
Same here.
#18
11-04-2003, 07:32 PM
 Macroman Member Join Date: Sep 2001 Location: you know where Favorite beer: Mountain Dew Posts: 3,843

Quote:
 Originally Posted by taaveez Unfortunately, my error was somewhere in the calculation of E(X) so although I got the right E(X^d), my E(X) was wrong. How about the one with a benefit level to be chosen to minimize the variance on a policy? I think I got something 150K for that one.
Bingo. The variance is minimized by having a death benefit equal to the value of the annuity. Since it's a perpetuity, APV = B/d.
#19
11-04-2003, 07:32 PM
 TenaciousMV Member SOA AAA Join Date: Nov 2002 Posts: 341

Quote:
 Originally Posted by Msta E(X) was .01 up to 80, then grade to 0 by 120. 80*.01 = .8 .01*(40)/2 = .2 E(X) = 1 and E(X^x) = .01*20 = .2 not 20
The "0.01" you refer to was the probability of those values. That's why it sums to 1.

The expected value is
(.8)*40 + (.2)*((80)+(1/3)*(120-80))
#20
11-04-2003, 07:35 PM
 eric Member Join Date: Oct 2003 Posts: 311

Did you guys get 34.44444 (which is 34 if you round it up) or 35 for the life expectancy question?