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  • Median Question.

    Can someone help me with this.

    An insurance policy reimburses dental expenses, X, up to a maximum benefit of 250. The probability density function for X is.


    F(x) = ce^(–0.004x) for x >= 0
    0 otherwise

    Where c is constant. Calculate the Median benefit for this policy.


    Ans: 173.2868
    Last edited by hinaahmad5; December 16 2005, 10:40 AM.

  • #2
    The density should probably be denoted f(x)
    (F(x) is generally used to denote the cumulative distribution function).
    Since c is a constant, the pdf must be f(x) = .004 e(^-.004x)
    in order for the integral from 0 to inf to be 1.
    We wish to find the median benefit payment.
    The benefit payment is the loss up to a max of 250.
    We first find the median of the expense is m, F(m) = .5 .
    The cdf is F(t) = 1 - e^(-.004t) , so the median of X satisfies
    1 - e^(-.004m) = .5 . Solving for m results in m = 173.3 .
    There is a 50% chance that the loss is <= 173.3 .
    Since this is below the deductible of 250, this is also
    the median benefit payment.
    Sam Broverman

    [email protected]
    www.sambroverman.com

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    • #3
      Are you in Professor Lieb's class at NJIT? I know we had that problem in our homework.

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      • #4
        Section 8.7, problem 20.

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        • #5
          Do I know you?

          I was reading your threads when I found out that you're a student at NJIT. I am a student at NJIT as well. I am a senior, actuarial science major. I might know you if you tell me your name.

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          • #6
            My previous message goes to SirVLCIV. I am new to this forum.

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            • #7
              I just finished my first semester at NJIT (transfer), with probability, linear algebra, calculus III, microeconomics, and accounting.
              Last edited by SirVLCIV; October 29 2012, 04:22 PM.

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