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SOA #33 ---- Random variable problem

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  • SOA #33 ---- Random variable problem

    The question is
    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) for 0<x<20 and o for otherwise
    Given the a fire loss exceeds 8, what is the probability that is exceeds 16?

    --------------
    My solution:
    P(x>16 | x>8) = P(x>16) / P(x>8)
    Take the integral from x to 20 of 0.005(20-t)dt which equals 0.005(20-x)

    but the solution manual says:
    The integral from x to 20 of 0.005(20-t)dt = 0.005(20t-1/2t^2)

    I don't understand where they got that from

  • #2
    never mind, i made a calc mistake

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