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  • median question

    The following is question from the sample SOA questions.

    The question was:

    An insurance policy reimburses dental expense, X, up to a maximum benefit of 250. The probability density function for X is: f(x) = ce^-0.004x for x>=0, o o.w
    where c is a constant. Find the median benefit for this policy.

    When I looked at the solution there was no place where they used the fact that the max benefit was 250. They simply integrated from 0-->m(f(x)). How would the solution to this question change so that we had to use the max benefit.

    Thank you.

  • #2
    Originally posted by audia4
    The following is question from the sample SOA questions.

    The question was:

    An insurance policy reimburses dental expense, X, up to a maximum benefit of 250. The probability density function for X is: f(x) = ce^-0.004x for x>=0, o o.w
    where c is a constant. Find the median benefit for this policy.

    When I looked at the solution there was no place where they used the fact that the max benefit was 250. They simply integrated from 0-->m(f(x)). How would the solution to this question change so that we had to use the max benefit.

    Thank you.
    Let's take a simpler problem. Suppose I let you pick any real number between 0 and 100 (decimals, fractions, etc. - anything). This is meant to simulate a uniform distribution on (0,100). So, it's natural to believe that 50 is the median, correct?

    Alright, now, suppose this was the distribution for life insurance claims (in thousands). So, the median claim is $50K. If we set a benefit amount limit greater than $50K, then the median will still be $50K - the probability that the benefit amount will be less than or equal to $50K = probability that the benefit amount will be greater than or equal to $50K = 0.5, which is the definition of a median. If we set the limit to be less than $50K, then we use the limit as the median, since both P(ben=>limit) and P(ben<=limit) are greater than 0.5, which is also a definition of the median.

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