Answer ALL questions Question 1 (a) Given the following information: A sample of 2000 claims contains 1700 claims that are no greater than $6,000, 30 claims that are greater than $6,000 but no greater than $7,000 and 270 claims that are greater than $7,000. (c) If a policy limit, u apply on to these claims, E[X Au]-total amount of claim paid Given E[X A $6,000] = 1810 number of claims The total amount of 30 claims that are greater than $6,000 but no greater than $7,000 is $200,000. Find E[X A $7,000] based on this sample. (b) You are given the following information: A large risk has a lognormal claim size distribution with parameter µ = 8.443 and o=1.239. The insurance agent for the risk settles all claims under $5,000. (Claims of $5,000 or more are settled by the insurer, not the agent.) Determine the expected value of claim per payment settled by the insurance agent. You are given the following: Based on observed data truncated from above at $10,000, the probability of a claim exceeding $3,000 is 0.30. Based on the underlying distribution of losses, the probability of a claim exceeding $10,000 is 0.02. Determine the probability that a claim exceeds $3,000 (original probability without the truncation applied).

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Answer ALL questions
Question 1
(a)
Given the following information:
●
A sample of 2000 claims contains 1700 claims that are no greater than $6,000, 30
claims that are greater than $6,000 but no greater than $7,000 and 270 claims that
are greater than $7,000.
If a policy limit, u apply on to these claims, E[X Au] total amount of claim paid
number of claims
Given E[X A $6,000] = 1810
The total amount of 30 claims that are greater than $6,000 but no greater than
$7,000 is $200,000.
Find E[X A $7,000] based on this sample.
(b) You are given the following information:
A large risk has a lognormal claim size distribution with parameter μ = 8.443 and
o = 1.239.
The insurance agent for the risk settles all claims under $5,000. (Claims of $5,000
or more are settled by the insurer, not the agent.)
Determine the expected value of claim per payment settled by the insurance agent.
(c) You are given the following:
Based on observed data truncated from above at $10,000, the probability of a
claim exceeding $3,000 is 0.30.
Based on the underlying distribution of losses, the probability of a claim
exceeding $10,000 is 0.02.
Determine the probability that a claim exceeds $3,000 (original probability without the
truncation applied).
Transcribed Image Text:Answer ALL questions Question 1 (a) Given the following information: ● A sample of 2000 claims contains 1700 claims that are no greater than $6,000, 30 claims that are greater than $6,000 but no greater than $7,000 and 270 claims that are greater than $7,000. If a policy limit, u apply on to these claims, E[X Au] total amount of claim paid number of claims Given E[X A $6,000] = 1810 The total amount of 30 claims that are greater than $6,000 but no greater than $7,000 is $200,000. Find E[X A $7,000] based on this sample. (b) You are given the following information: A large risk has a lognormal claim size distribution with parameter μ = 8.443 and o = 1.239. The insurance agent for the risk settles all claims under $5,000. (Claims of $5,000 or more are settled by the insurer, not the agent.) Determine the expected value of claim per payment settled by the insurance agent. (c) You are given the following: Based on observed data truncated from above at $10,000, the probability of a claim exceeding $3,000 is 0.30. Based on the underlying distribution of losses, the probability of a claim exceeding $10,000 is 0.02. Determine the probability that a claim exceeds $3,000 (original probability without the truncation applied).
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