'3. (4 POINTS) The claim amount (in S) for a health insurance policy is a random variable with probability density function
flx) = (1/1000) exp (-x/1000) ifx > 0; flx) = 0, otherwise.
The premium for this policy is set at S100 over the expected total claim amount If 100 policies are sold, what is the approximate probability that the insurance company will have total claims exceeding the total premiums collected?
Hint: Let X denote the claim amount for a randomly selected policy: Verify that E(X) 1,000. The premium for a single policy is 100 E(X) = 1,100.'