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Error of a simulated probability

ProbabilityMedium

A barrier is hit with true probability $0.1$ on each independent path. A simulation of $900$ paths estimates this probability by the share of paths that hit. What is the standard error of that estimate? Answer as a decimal.

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Hint

One hit indicator has variance $p (1 - p)$ .

Solution

One indicator has variance $0.1 \times 0.9 = 0.09$ , and its root is $0.3$ .
With $900$ paths, whose root is $30$ , the standard error is $\frac{0.3}{30} = 0.01$ , so the answer is $0.01$ .

Answer: $0.01$

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