2016 Mahler E5 Q14

this is an expected payment per payment question with 0 < x < 1200. ordinary deductible of 500. pay 90% of loss above deductible. policy limit of 450.

I need help understanding the following integral:
0.9 * integral from 500 to 1000 of S(x) dx

when I originally solved this question, I calculated the following:
(1) ... integral from 500 to 1000 of 0.9(x-500)*f(x) dx
(2) ... 450* Pr(X>1000)
(3) ... Pr(X>500)

(1 + 2)/3 = correct answer

how does "0.9 * integral from 500 to 1000 of S(x) dx" account for a payment of 450 when the loss is between 1000 - 1200? yay calculus


2016 Mahler E5 Q14