IAI Actuarial Core Principles · Actuarial Statistics · Basic univariate distributions and generating samples
A simulation estimates the probability p that an annual loss exceeds Rs 50 crore. Out of 2,500 independent runs, 200 exceed Rs 50 crore. What is the approximate standard error of the estimated probability?
The standard error is about 0.0054. The estimated probability is 0.08, and the standard error is the square root of p times (1 minus p) divided by n, which is the square root of 0.0736 over 2,500, giving roughly 0.0054.
- A0.0054Correct
- B0.0080
- C0.0160
- D0.0736
- 0.0800
Explanation
p-hat = 200/2500 = 0.08. SE = sqrt(0.08 x 0.92/2500) = sqrt(0.0000294) = 0.00543. 0.0160 comes from omitting the square root of n incorrectly, and 0.0736 is just p(1-p).
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