Calculating a median reimbursement of a policy under a policy limit.

Question

An insurance policy reimburses losses incurred by a policyholder subject to a limit of 1000. Losses follow an exponential distribution with mean 500.

Calculate the median reimbursement for this policy.

a.) 26 b.) 347 c.) 490 d.) 504 e.) 750

Answer 1

Hint:

Let $X$ be the loss incurred such that $X\sim\mathrm{Exp}(1/500)$.

Let $Y$ be the payout.

What can you say about the distribution of $Y$ for $x<1000$? What can you say about the distribution of $Y$ for $x\ge1000$?

At which range does $F_Y(y)=0.5$?