central-limit-theorem #

Simulates standardized sums Zₙ of many i.i.d. random variables from different base distributions (uniform, ±1, shifted exponential) and shows how the histogram of Zₙ approaches the overlaid standard normal curve N(0,1) as n increases. Side panels emphasize the CLT conditions (independence, finite variance) and the standardization step (centering by nμ and scaling by σ√n).

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⏮◀◀▶▶STEP0.25x1xZOOM

t=0s

practical uses #

01.Justifying normal approximations for sums/averages in quality control and measurement error
02.Building confidence intervals and hypothesis tests for means when n is moderately large
03.Explaining why many aggregated signals/noises look Gaussian even when individual components are not

technical notes #

Per-frame Monte Carlo sampling updates a 64-bin histogram over z∈[-4,4] with exponential forgetting and light 1D smoothing. The visualization cycles through n values (1→100) and base distributions, overlaying the analytic N(0,1) density for comparison. All drawing is grid-snapped for a blocky aesthetic and uses only the Canvas 2D API.

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