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Question 11.6: Suppose the insurance company includes a deductible of 5 on ......

Suppose the insurance company includes a deductible of 5 on annual claim payments for each member. Determine the expected claims payments and standard deviation for the pool.

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There are three cases to consider:

a. No hospitalization and so no claim payments
b. Hospitalization but charges less than the deductible
c. Hospitalization but charges more than the deductible

E\left[Y\right]=P\left(H\neq1\right)E\left[Y\mid H\neq1\right]+P\left(X\leq5,\,H=1\right)E\left[Y\mid X\leq5,\,H=1\right]+~P(X\gt 5,~H=1)E[Y\mid~X\gt 5,~H=1].

The calculation results in E[Y] = 0.91 and \sigma_{Y}^{2} = 17.37, we have \sigma_{X} = √17.37 = 4.17.

The details are in [Rsa:05].

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