In a group of 25 health insurance policyholders diagnosed with cancer, each poli

Q: In a group of 25 health insurance policyholders diagnosed with cancer, each poli

Solution Let R be the amount paid by insurance company for the radiation and C be the amount paide by insurance company for chemotherapy Var(R+C) = V(R)+V(C)=2Cov(R,C) V(R) = E(R2) - E(R)2 = (4*0.9)-(2*0.9)2 = 0.36 V(C) = 9*0.4 - (3*0.4)2 = 2.16 Cov(R,C) = 0 25*V(R) = 25*(0.36+2.16) = 63

ID: 3326507 • Letter: I

Question

In a group of 25 health insurance policyholders diagnosed with cancer, each policyholder has probability 0.90 of receiving radiation and probability 0.40 of receiving chemotherapy. Radiation and chemotherapy treatments are independent events for each policyholder, and the treatments of different policyholders are mutually independent. The policyholders in this group all have the same health insurance that pays 2 for radiation treatment and 3 for chemotherapy treatment. Calculate the variance of the total amount the insurance company pays for the radiation and chemotherapy treatments for these policyholders.

Explanation / Answer

Solution

Let R be the amount paid by insurance company for the radiation

and C be the amount paide by insurance company for chemotherapy

Var(R+C) = V(R)+V(C)=2Cov(R,C)

V(R) = E(R2) - E(R)2 = (4*0.9)-(2*0.9)2 = 0.36

V(C) = 9*0.4 - (3*0.4)2 = 2.16

Cov(R,C) = 0

25*V(R) = 25*(0.36+2.16) = 63

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In a group of 25 health insurance policyholders diagnosed with cancer, each poli

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