Tag Archives: Pure Premium

Exam C Practice Problem 2 – Variance of Pure Premium

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.

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      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 135

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 8,650

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 9,694

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 10,296

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 18,250

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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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      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 310

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 7,189

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 7,236

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 7,719

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 96,100

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\copyright \ 2013 \ \ \text{Dan Ma}