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V=220 L+451 H
The sample variance, 
V, in the expected total premiums of 
L lowrisk beneficiaries and 
H high-risk beneficiaries based on an underwriter's premium allocation is given by the equation. The values of 
L and 
H are independent. What is the best interpretation of 
451H as shown in the equation?
Choose 1 answer:
(A) There are 
451 H high-risk beneficiaries.
(B) The total variance due to high-risk beneficiaries is 
451H.
(C) The variance in premiums for a high-risk beneficiary is 
451H.
(D) The expected total premiums for high-risk beneficiaries is 
451H.

V=220L+451H V=220 L+451 H \newlineThe sample variance, V V , in the expected total premiums of L L lowrisk beneficiaries and H H high-risk beneficiaries based on an underwriter's premium allocation is given by the equation. The values of L L and H H are independent. What is the best interpretation of 451H 451 \mathrm{H} as shown in the equation?\newlineChoose 11 answer:\newline(A) There are 451H 451 H high-risk beneficiaries.\newline(B) The total variance due to high-risk beneficiaries is 451H 451 \mathrm{H} .\newline(C) The variance in premiums for a high-risk beneficiary is 451H 451 \mathrm{H} .\newline(D) The expected total premiums for high-risk beneficiaries is 451H 451 \mathrm{H} .

Full solution

Q. V=220L+451H V=220 L+451 H \newlineThe sample variance, V V , in the expected total premiums of L L lowrisk beneficiaries and H H high-risk beneficiaries based on an underwriter's premium allocation is given by the equation. The values of L L and H H are independent. What is the best interpretation of 451H 451 \mathrm{H} as shown in the equation?\newlineChoose 11 answer:\newline(A) There are 451H 451 H high-risk beneficiaries.\newline(B) The total variance due to high-risk beneficiaries is 451H 451 \mathrm{H} .\newline(C) The variance in premiums for a high-risk beneficiary is 451H 451 \mathrm{H} .\newline(D) The expected total premiums for high-risk beneficiaries is 451H 451 \mathrm{H} .
  1. Equation Representation: The equation V=220L+451HV = 220L + 451H represents the sample variance in expected total premiums for LL low-risk and HH high-risk beneficiaries.
  2. Low-risk Contribution: The term 220L220L suggests that each low-risk beneficiary contributes 220220 units to the variance.
  3. High-risk Contribution: Similarly, the term 451H451H suggests that each high-risk beneficiary contributes 451451 units to the variance.
  4. Total Variance: Therefore, 451H451H represents the total variance due to all HH high-risk beneficiaries.

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