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SOA exam P question #33

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  • SOA exam P question #33

    The loss due to a fire in a commercial building is modeled by a random variable X
    with density function

    f(x)={0.005(20-x) 0<x<20
    { 0 otherwise
    Given that a fire loss exceeds 8, what is the probability that it exceeds 16

    In the solution, why is it that the integral goes from x to 20???

  • #2
    Did you draw a picture?

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    • #3
      P(x>16|x>8) = P(x>16)/P(x>8). Because the domain of x is from 0 to 20. It is understood that the upper limit of the integral is 20.
      P(x>16) = P(16<x<20) etc.

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      • #4
        Consider what would happen if after you computed the integral you plugged in 8 for x. That is the same as integrating from 8 to 20.

        Integrating from x to 20 saves you an extra step since you must compute P(x>16) and P(x>20). You simply integrate from x to 20 and then plug in the lower bound as x in your answer.

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        • #5
          Hi. I'm new to this forum. I have few questions about these exams that needed to be taken in order to become an actuary. where do you get the studying materials? I took Probability/Statistics class in college, will that be enough to pass the Probability exam? what studying materials are good out there? do you go to school to gain more training to pass the exams? Thank you so much for helping me. btw, nice meeting everyone :-)

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          • #6
            Originally posted by nini1021 View Post
            Hi. I'm new to this forum. I have few questions about these exams that needed to be taken in order to become an actuary. where do you get the studying materials? I took Probability/Statistics class in college, will that be enough to pass the Probability exam? what studying materials are good out there? do you go to school to gain more training to pass the exams? Thank you so much for helping me. btw, nice meeting everyone :-)
            You probably should've started a new thread instead of replying to one about an exam question but anyways, check out beanactuary.com and do some research

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