The total claim amount for a health insurance policy follows a distribution with density
function f(x) = 11000e−x/1000, for x > 0.The premium for the policy is set at 100 over the expected total claim amount. If 100
policies are sold, what is the approximate probability that the insurance company will
have claims exceeding the premiums collected?
it's obvious that there's a typo in the expression of the density function.
f(x) = (1/1000) e^(-x/1000) should be the correct density,
otherwise, it is NOT a probability density.
with that, E[X]=1000, and "The premium for the policy is set at 100 over the expected total claim amount"
therefore, premium = 1000+100=1100.
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