Please refer to the following question in the ACTEX Manual (Practice Exam 1 Qn.12) and also in the SOA sample exam P-09-05 Qn.68:
An insurance policy reimburses dental expense, X, up to a maximum benefit of 250 . The probability density function for X is:
f(x) = ce**-.004x for x>=0
= 0 otherwise
where c is a constant.
Calculate the median benefit for this policy.
The correct answer is, of course, 173. It is arrived at by integrating f(x) from 0 to m and equating it to 0.5. However, if, say, the maximum benefit was 100 (instead of 250), would not the median benefit be different? What I am trying to say is that the calculation of median 'benefit' must involve using the maximum benefit amount also. Does this make sense or is it just my overworked gray matter exploding into nonsense?