Exam P Practice Problem 99 – When Random Loss is Doubled
Problem 99A
A business owner faces a risk whose economic loss amount follows a uniform distribution over the interval . In the next year, the loss amount is expected to be doubled and is expected to be modeled by the random variable .
Suppose that the business owner purchases an insurance policy effective at the beginning of next year with the provision that any loss amount less than or equal to 0.5 is the responsibility of the business owner and any loss amount that is greater than 0.5 is paid by the insurer in full. When a loss occurs next year, determine the expected payment made by the insurer to the business owner.
Problem 99B
A business owner faces a risk whose economic loss amount has the following density function:
In the next year, the loss amount is expected to be doubled and is expected to be modeled by the random variable .
Suppose that the business owner purchases an insurance policy effective at the beginning of next year with the provision that any loss amount less than or equal to 1 is the responsibility of the business owner and any loss amount that is greater than 1 is paid by the insurer in full. When a loss occurs next year, what is the expected payment made by the insurer to the business owner?
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probability exam P
actuarial exam
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Daniel Ma
mathematics
expected insurance payment
deductible
2017 – Dan Ma
Exam P Practice Problem 96 – Expected Insurance Payment
Problem 96A
An insurance policy is purchased to cover a random loss subject to a deductible of 1. The cumulative distribution function of the loss amount is:
Given a random loss , determine the expected payment made under this insurance policy.
Problem 96B
An insurance policy is purchased to cover a random loss subject to a deductible of 2. The density function of the loss amount is:
Given a random loss , what is the expected benefit paid by this insurance policy?
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Exam P Practice Problem 92 – Expected Claim Payment
Problem 92A
The size of a claim that an auto insurance company pays out is modeled by a random variable with the following density function:
By subjecting the insured to a deductible of 12 per claim, what is the expected reduction in claim payment?
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Problem 92B
The size of a claim that an auto insurance company pays out is modeled by a random variable with the following density function:
By subjecting the insured to a deductible of 10 per claim, by what percent is the expected claim payment reduced?
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Exam P Practice Problem 90 – Insurance Benefits
Problem 90A
A random loss follows an exponential distribution with mean 20. An insurance reimburses this random loss up to a benefit limit of 30.
When a loss occurs, what is the expected value of the benefit not paid by this insurance policy?
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Problem 90B
A random loss follows an exponential distribution with mean 100. An insurance reimburses this random loss up to a benefit limit of 200.
When a loss occurs, what is the expected value of the benefit not paid by this insurance policy?
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Exam P Practice Problem 88 – Expected Value of Insurance Payments
Problem 88A
A random loss has a uniform distribution over the interval . An insurance policy is purchased to reimburse the loss up to a maximum limit of where .
The expected value of the benefit payment under this policy is 8.4. Calculate the value of .
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Problem 88B
An individual purchases an insurance policy to cover a loss whose density function is:
The insurance policy reimburses the policy owner up to a benefit limit of 4 for each loss. What is the expected value of insurance payment made to the policy owner?
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Exam P Practice Problem 84 – When Random Loss is Doubled
Problem 84A
A business owner faces a risk whose economic loss amount follows a uniform distribution over the interval . In the next year, the loss amount is expected to be doubled and is expected to be modeled by the random variable .
Suppose that the business owner purchases an insurance policy effective at the beginning of next year with the provision that any loss amount less than or equal to 0.5 is the responsibility of the business owner and any loss amount in excess of 0.5 is the responsibility of the insurer. When a loss occurs next year, what is the expected payment made by the insurer to the business owner?
Problem 84B
A business owner faces a risk whose economic loss amount has the following density function:
In the next year, the loss amount is expected to be doubled and is expected to be modeled by the random variable .
Suppose that the business owner purchases an insurance policy effective at the beginning of next year with the provision that any loss amount less than or equal to 1 is the responsibility of the business owner and any loss amount in excess of 1 is the responsibility of the insurer. When a loss occurs next year, what is the expected payment made by the insurer to the business owner?
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Answers

Answers can be found in this page.
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