FRM Part I · FRM Exam Part I · Fundamentals of Probability
An insurer's claim count N has the following distribution: P(N=0)=0.5, P(N=1)=0.3, P(N=2)=0.2. What is Var(N)?
Var(N) is 0.61. The mean is 0(0.5)+1(0.3)+2(0.2) = 0.7, and E[N^2] = 1(0.3)+4(0.2) = 1.1. Variance equals E[N^2] minus the squared mean: 1.1 - 0.49 = 0.61.
- A0.61Correct
- B0.70
- C0.49
- D0.90
Explanation
E[N] = 0.3 + 0.4 = 0.7. E[N^2] = 0.3(1) + 0.2(4) = 1.1. Var = 1.1 - 0.49 = 0.61. The option 0.49 is the squared mean, and 0.70 is the mean itself.
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