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Long-Term Actuarial Math Old Exam MLC Forum

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  #11  
Old 11-04-2003, 06:16 PM
Msta Msta is offline
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The one with the LER? I got .2.

E(X^x) = .2
E(X) = 1
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  #12  
Old 11-04-2003, 06:18 PM
sleg sleg is offline
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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  
Old 11-04-2003, 06:19 PM
taaveez taaveez is offline
 
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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.
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  #14  
Old 11-04-2003, 06:21 PM
TenaciousMV TenaciousMV is offline
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I agree that (X^x)=20, but E(x) isn't 100... it's more like 55-60.

My answer was around .36
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  #15  
Old 11-04-2003, 06:24 PM
Msta Msta is offline
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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
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  #16  
Old 11-04-2003, 06:26 PM
taaveez taaveez is offline
 
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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.
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  #17  
Old 11-04-2003, 06:29 PM
Rhizome Rhizome is offline
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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.
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  #18  
Old 11-04-2003, 06:32 PM
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Macroman Macroman is offline
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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.
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  #19  
Old 11-04-2003, 06:32 PM
TenaciousMV TenaciousMV is offline
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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))
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  #20  
Old 11-04-2003, 06:35 PM
eric eric is offline
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Did you guys get 34.44444 (which is 34 if you round it up) or 35 for the life expectancy question?
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