IAI Actuarial Core Principles · Actuarial Statistics · Basic univariate distributions and generating samples
A discrete claim count N has P(N=0)=0.4, P(N=1)=0.3, P(N=2)=0.2, P(N=3)=0.1. Five Uniform(0,1) values 0.15, 0.62, 0.95, 0.40, 0.71 are used with the inverse transform method, assigning N=k when F(k-1) <= u < F(k) (so 0.40 gives N=1). What is the sum of the five simulated counts?
The sum is 7. With cumulative probabilities 0.4, 0.7, 0.9 and 1.0, the uniforms map to 0, 1, 3, 1 and 2 respectively, using the stated boundary rule for 0.40, and these add to 7.
- A7Correct
- B6
- C8
- D5
- 9
Explanation
Cumulative probabilities are 0.4, 0.7, 0.9, 1.0. u=0.15→0; 0.62→1; 0.95→3; 0.40→1 (as specified); 0.71→2. Sum = 0+1+3+1+2 = 7. Treating 0.40 as 0 would give 6, which ignores the stated boundary rule.
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