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#11




The one with the LER? I got .2.
E(X^x) = .2 E(X) = 1 
#12




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#13




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. 
#15




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




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




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#18




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#19




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The expected value is (.8)*40 + (.2)*((80)+(1/3)*(12080)) 
#20




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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