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Exam P Question - integration problem

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  • Exam P Question - integration problem

    Here's the question:
    An insurance policy is written to cover loss X where f(x)=(3/8)*x^2. The time (in hrs) to process a claim of size x, where 0<x<2, is uniformly distributed from x to 2x. Find P(T>3)?

    I've seen two solutions to this problem that are nearly identical with the exception of the double integrals' boundaries. Variables are used for certain integration limits.

    I don't see why a variable is needed in the final steps of integration. Why can't we simply use a double integral from 1.5 to 2 for dx & 3 to 4 for dt.

    I'm not very savvy when it comes to integration and don't have a ton of practice with it, am I may be missing something obvious, my results don't yield .17

    I get .328