That is two chances to get one right. Or two chances to get two right, or...

]]>1. I made a mistake assuming density function is 0 beyond x = 250- it is clearly 250

2. Clearly, if the median for the exponential density function works out to be less than the benefit limit, the limit doesnt change the median

Thanks bobbym! I got 2 more problems for you - Stay tuned!

]]>This problem appears on every actuary exam. See if these help you. These sites have some reasons why it must be .004.

http://docs.google.com/viewer?a=v&q=cac … dmqmMRl8kA

]]>integral (0.004 e ^ -0.004*x ) over [0, x ] = 0.5 -works out to 173.4

However, since it mentioned maximum benefit of 250, to determine c, I used -

integral (pdf) over [0, 250] = 1 - this gives c of 0.00633

and then solving the same equation above for x gives 94.97

]]>Thanks but I think you are overestimating me. Can I see what you did to get 94?

Did you get .004 for c?

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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,

0 otherwise,

where c is a constant. Calculate the median benefit for this policy.

(A) 161 (B) 165 (C) 173 (D) 182 (E) 250

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My question is -

When the question states the maximum benefit is 250 units, shouldnt the benefit density function be the value for f(x) only until 250 and 0 beyond?

I ask as this changes the answer. With benefit density limited to 250 (as the question states), my median calculation is around 94. Withouth the 250 unit limitation, the median works out to be 173 (Option - C) which matches the solution in my textbook.

Why is the solution not accounting for 250 unit limit? Any ideas?

THANKS IN ADVANCE BOBBYM!!!

- G

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