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Artikel ieu bakal ngajelaskeun ilustrasi central limit theorem.

Fungsi probabilitas densiti (PDF) ditembongkeun dina gambar kahiji.

Saterusna jumlah densitas dua, tilu jeung opat variabel bebas, unggal densiti aslina, ditembongkeun dina gambar saterusna.

Sanajan densiti aslina jauh tina normal, jumlah densiti nu variabelna saeutik nu densitina leuwih lemes jeung sababaraha di antara nembongkeun densiti normal.

A more concrete illustration, in which most of the arithmetic can be done more-or-less instantly by hand, is at concrete illustration of the central limit theorem. There is also a free full-féatured interactive simulation available which allows you to set up various distributions and adjust the sampling paraméters (see "external links" at the bottom of this page).

The densities of the sums of two, three, and four terms were constructed as the convolution of the original density with itself.

As the original density is a piecewise polynomial (of degree 0 and 1),

the convolutions are also piecewise polynomials,