Exam P Practice Problem 102 – estimating claim costs
Problem 102A
Insurance claims modeled by a distribution with the following cumulative distribution function.
The insurance company is performing a study on all claims that exceed 3. Determine the mean of all claims being studied.
Problem 102B
Insurance claims modeled by a distribution with the following cumulative distribution function.
The insurance company is performing a study on all claims that exceed 4. Determine the mean of all claims being studied.
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actuarial exam
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Daniel Ma actuarial
2018 – Dan Ma
Exam P Practice Problem 97 – Variance of Claim Sizes
Problem 97A
For a type of insurance policies, the following is the probability that the size of claim is greater than .
Calculate the variance of the claim size for this type of insurance policies.
Problem 97B
For a type of insurance policies, the following is the probability that the size of a claim is greater than .
Calculate the expected claim size for this type of insurance policies.
probability exam P
actuarial exam
math
Daniel Ma
mathematics
Answers

Answers can be found in this page.
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 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 86 – Finding Mean and Variance
The following is the cumulative distribution function of the random variable .
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Problem 86A
Calculate the expected value of .
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Problem 86B
Calculate the variance of .
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Answers

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Exam P Practice Problem 77 – Estimating Random Claim Sizes
Problem 77A
The probability distribution of the claim size from an auto insurance policy randomly selected from a large pool of policies is described by the following density function.
What is the probability that a randomly selected claim from this insurance policy is within 120% of the mean claim size?
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Problem 77B
The probability distribution of the claim size from an auto insurance policy randomly selected from a large pool of policies is described by the following density function.
What is the probability that a randomly selected claim from this insurance policy is within onehalf of a standard deviation of the mean claim size?
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Exam P Practice Problem 76 – Quantifying Average Random Loss
Both Problem 76A and Problem 76B use the following information.
A property owner faces a series of independent random losses. Each loss is either 10 (with probability 0.4) or 50 (with probability 0.6).
Three such random losses are selected.
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Problem 76A
What is the probability that the mean of the three losses is less than 30?
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Problem 76B
What is the expected value of the mean of the three losses?
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Exam P Practice Problem 75 – Travel Time to Work By Train
Both Problem 75A and Problem 75B use the following information.
A worker travels to work by train 5 days a week (Monday to Friday). The length of a train ride (in minutes) to work follows a continuous uniform distribution from 10 to 40.
The lengths of the train ride across the days of the week are independent.
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Problem 75A
What is the probability that the shortest train ride during a work week is between 15 and 20 minutes?
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Problem 75B
What is the expected value of the longest train ride during a work week?
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Exam P Practice Problem 74 – Review of Auto Insurance Claims
Both Problem 74A and Problem 74B use the following information.
An insurer issued policies to cover a large number of automobiles. Claim amounts (in thousands) from these policies are independent and are modeled by a continuous uniform distribution on (0,10).
The insurer randomly selects five claims for review.
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Problem 74A
What is the probability that the minimum claim amount is between 2 thousands and 6 thousands?
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Problem 74B
What is the expected value of the maximum claim amount?
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Exam P Practice Problem 73 – Wait Time at a Busy Restaurant
Both Problem 73A and Problem 73B use the following information.
A certain restaurant is very busy in the evening time during the weekend. When customers arrive, they typically have to wait for a table.
When a customer has to wait for a table, the wait time (in minutes) follows a distribution with the following density function.
A customer plans to dine at this restaurant on five Saturday evenings during the next 3 months. Assume that the customer will have to wait for a table on each of these evenings.
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Problem 73A
What is the probability that the minimum wait time for a table during the next 3 months for this customer will be more than half an hour?
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Problem 73B
What is the mean of the maximum wait time (in minutes) for a table during the next 3 months for this customer?
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