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Thread: CDF of a PDF with a negative power

  1. #1
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    CDF of a PDF with a negative power

    I need to solve the following problem:

    For a marine hull insurance policy, a claim occurs with probability 0.DD, where DD represents the two date-digits of your birthday (DD.MM.YYYY). If a claim occurs, it has a probability density given by

    fB(x)=cx^(−1.5), 1<x<YYYY,

    where YYYY are the four digits of your birth year and c is a constant to be determined. Determine the c.d.f. and the first two moments of both B (the claim given it occurs) and X (the payment to the policy). Plot the two c.d.f.s.

    I set that the integral of my pdf from 1 to YYYY has to be equal to 1, so I found c.

    But the problem is that when I integrate the pdf in order to find the cdf, I have a negative cdf, which cannot be. How do you deal with negative power in a pdf ?

  2. #2
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    Re: CDF of a PDF with a negative power

    Did you put in the limits of integration from 1 to 2000 or whatever? It will come out positive because it is all above the x axis.

  3. #3
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    Dason's Avatar
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    Re: CDF of a PDF with a negative power

    Why don't you tell us what you got for c and what you think the cdf is.
    I don't have emotions and sometimes that makes me very sad.

  4. #4
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    Dragan's Avatar
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    Re: CDF of a PDF with a negative power

    It would seem to me that you might want to consider integrating the function (i.e. solving for the constant ("c") from 1 to Infinity; which gives the result for "c" that will provide the pdf and cdf. In terms of moments, you have to specify a finite upper limit (e.g. 2000 as suggested above) because the integral will (theoretically) fail to converge to infinity.

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