In a group of 20 health insurance policyholders diagnosed with cancer, each policyholder has probability 0.80 of receiving radiation and probability 0.35 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 2 000 for radiation treatment and 3 0000 for chemotherapy treatment. Calculate the variance of the total amount the insurance company pays for the radiation and chemotherapy treatments for these 20 policyholders.

MATLAB: An Introduction with Applications
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In a group of 20 health insurance policyholders diagnosed with cancer, each policyholder
has probability 0.80 of receiving radiation and probability 0.35 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 2 000 for radiation treatment and
3 0000 for chemotherapy treatment.
Calculate the variance of the total amount the insurance company pays for the radiation
and chemotherapy treatments for these 20 policyholders.

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