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Medium · Numerical Methods & Monte Carlo · Numerical · ~6 min · #44

Standard Error of a Monte Carlo π

You estimate π\pi by sampling N=10,000N = 10{,}000 points uniformly in the unit square and computing π^=4×(fraction with x2+y2≤1)\hat\pi = 4 \times (\text{fraction with } x^2 + y^2 \leq 1).

What is the standard error of π^\hat\pi? Answer to three significant figures.

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Monte Carlo errorSquare-root convergence

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