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.

\text{ }

      \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.

\text{ }

      \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}

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