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ShortTerm Actuarial Math Old Exam C Forum 

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#1




SOA #87
Looking at the 6th line in the solution, i.e. E(X20)+ = E(X)  ....
I understand that this line is using the formula E[(X20)+] = E(X)  E[(X^20)], but how does that second part of the 6th line equate to E[(X^20)]?? And for this particular question, can I use the survival function (derived by finding the distribution function F(x) from the f(x) in the solution and then S(x)= 1  F(x)), and then integrating the survival function from 20 to 80 for the flat f(x) portion + integrating the survival function from 82 to 120 for the declining f(x) portion? Thank you! 
#2




Whenever X is a continuous loss variable,
In their expression, they are finding Pr[X>20] by doing 1  Pr[X<=20] as the integral for P[X<=20] is easier than the integral for Pr[X>20]. Yes, you could use the survival function. I think it will take longer. 
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