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world:definetti
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world:definetti [2026/02/03 16:14] rdouc ↷ Links adapted because of a move operation |
world:definetti [2026/02/03 19:01] (current) rdouc |
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| - | {{page>:defs}} | + | on{{page>:defs}} |
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| \frac1{n(n-1)\cdots(n-k+1)} | \frac1{n(n-1)\cdots(n-k+1)} | ||
| \sum_{\substack{1\le i_1,\ldots,i_k\le n\\ i_j\neq i_\ell}} | \sum_{\substack{1\le i_1,\ldots,i_k\le n\\ i_j\neq i_\ell}} | ||
| - | f(X_{i_1},\ldots,X_{i_k}) + 0\lr{\frac1n} = \frac1{n^k}\sum_{i_1=1}^n\cdots\sum_{i_k=1}^n f(X_{i_1},\ldots,X_{i_k}). | + | f(X_{i_1},\ldots,X_{i_k}) + O\lr{\frac1n} = \frac1{n^k}\sum_{i_1=1}^n\cdots\sum_{i_k=1}^n f(X_{i_1},\ldots,X_{i_k}). |
| $$ | $$ | ||
| * Hence, for product functions $f(x_1,\ldots,x_k)=f_1(x_1)\cdots f_k(x_k)$, | * Hence, for product functions $f(x_1,\ldots,x_k)=f_1(x_1)\cdots f_k(x_k)$, | ||
world/definetti.1770131697.txt.gz · Last modified: 2026/02/03 16:14 by rdouc
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