**Problem 2-A**

You are given:

- For a given risk, the number of claims in a calendar year is 0 (with probability 0.4), 1 (with probability 0.5) and 2 (with probability 0.1).
- In case of only 1 claim, the claim size will be 100 (with probability 0.75) and 200 (with probability 0.25).
- In case of 2 claims, the claim size will be 100 (with probability 0.5) and 200 (with probability 0.5). The two claim sizes are independent.

Calculate the variance of the pure premium for this risk.

**Problem 2-B**

You are given:

- For a given risk, the number of claims in a calendar year is 0 (with probability 0.4), 1 (with probability 0.5) and 2 (with probability 0.1).
- The claim size will be 100 (with probability 0.75) and 200 (with probability 0.25).
- The number of claims and the claim size are independent.
- In case of 2 claims, the two claim sizes are independent.

Calculate the variance of the pure premium for this risk.

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Tagged: Actuarial Exam, CAS Exam 4, CAS Exam 4 Practice Problem, Frequency, Loss Models, Probability, Pure Premium, Severity, SOA Exam C, SOA Exam C Practice Problem, Variance

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