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#51 in SOA practice problems

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  • #51 in SOA practice problems

    51. A manufacturer’s annual losses follow a distribution with density function
    2.5(0.6) ( ) for 0.6
    0 otherwise.
    f x x x

    ⎪ > =⎨⎪⎩
    To cover its losses, the manufacturer purchases an insurance policy with an annual
    deductible of 2.
    What is the mean of the manufacturer’s annual losses not paid by the insurance policy?

    I have similar steps to the solution. Instead of Y=2, for x>2, I had Y=2 for x>.74 which I obtained from solving for x when Y=2. So that when x is between .6 & .74, the loss is just C and when x is greater than .74, the loss is x. Followed this through with expected value, integral(C*Y(x),x,.6,.74) + integral(X*Y(x),x,.74,inf).

    Why is this incorrect & could someone clarify the steps in the solution?

  • #2
    bump, need help PLZ

    Can anyone help me really soon plzz? My exam is tomorrow


    • #3
      What you wrote doesn't make sense. X is the amount of the loss, what significance does x such f(x) = 2 have for you? You found that a loss of .74 has a likelihood of 2.


      • #4
        The solution is something that you, probably, have seen in daily life.

        Imagine you have a healthcare policy with deductible 2 which means you as the insured will only pay up to 2 dollars.

        the loss is 1, you pay 1,
        the loss is .88, you pay .88
        the loss is 2.4, you pay 2
        the loss is 10 billion, you pay 2

        So how do you find your expected loss? Well from def. of expected value

        E(loss) = integral(or sum) of loss * probability of loss.

        However here loss is a piecewise function:

        1) between .6 and 2, you pay whatever the loss is i.e. X

        2) between 2 and infinity, you pay only 2

        Translate that into integrals you get:

        integral(x*f(x) dx from .6 to 2) + integral(2*f(x) dx from 2 to infinity)


        • #5
          Originally posted by DukeNCAA2010 View Post
          Can anyone help me really soon plzz? My exam is tomorrow
          Make sure you study "Risk and Insurance" at the end of

          Good luck!


          • #6

            Thanks for the help