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Soa #120

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  • Soa #120

    For some reason this problem throws me off. If someone could lead me in the right direction that would be great. The solution makes a little bit of sense but I guess I am confused on why we make it a joint density. This is probably a really dumb question but I am just thrown off by this.

    An insurance policy is written to cover a loss X where X has density function
    f(x) =(3/8)x^2 for 0<x<2 0 elsewhere

    The time (in hours) to process a claim of size x, where 0 ≤ x ≤ 2, is uniformly distributed
    on the interval from x to 2x.
    Calculate the probability that a randomly chosen claim on this policy is processed in three
    hours or more.

  • #2
    It is a joint pdf, more precisely a conditional pdf, a result of the formula P(EF)=P(F)P(E|F), where P(F)=3x^2/8 and P(E|F)=1/x, each with applicable domain.

    Cheers.
    P(7/09) FM(8/09)

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    • #3
      thanks a lot

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      • #4
        this probably one of the hardest questions on the list in terms of annoyingness and length.

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