求解：the premium for the policy is set at 100 over the expected total claim amt

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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?

为什么premium for each policy is 1100, 谢谢

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关键词：Expected premium expect Policy Total set expected policy

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.

IntheRed 发表于 2013-3-11 10:09
it's obvious that there's a typo in the expression of the density function.
f(x) = (1/1000) e^(-x/1 ...

I‘ve got it. Thx!