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Diffstat (limited to 'Master/texmf-dist/doc/fonts/fbb/fbb-doc.tex')
-rw-r--r-- | Master/texmf-dist/doc/fonts/fbb/fbb-doc.tex | 4 |
1 files changed, 2 insertions, 2 deletions
diff --git a/Master/texmf-dist/doc/fonts/fbb/fbb-doc.tex b/Master/texmf-dist/doc/fonts/fbb/fbb-doc.tex index b989f293279..aa2f19c7710 100644 --- a/Master/texmf-dist/doc/fonts/fbb/fbb-doc.tex +++ b/Master/texmf-dist/doc/fonts/fbb/fbb-doc.tex @@ -76,10 +76,10 @@ and $\uppi$. (The first two are entered as \verb|\mathrm{d}| and \textbf{Simplest form of the \textit{Central Limit Theorem}:} \textit{Let $X_1$, $X_2,\cdots$ be a sequence of iid random variables with mean $0$ and variance $1$ on a probability space $(\Omega,\mathcal{F},\Pr)$. Then} -\[\Pr\Big(\frac{X_1+\cdots+X_n}{\sqrt{n}}\le y\Big)\to\mathfrak{N}(y):= +\[\Pr\left(\frac{X_1+\cdots+X_n}{\sqrt{n}}\le y\right)\to\mathfrak{N}(y)\coloneq \int_{-\infty}^y \frac{\mathrm{e}^{-t^2/2}}{\sqrt{2\uppi}}\, \mathrm{d}t\quad\mbox{as $n\to\infty$,}\] -\textit{or, equivalently, letting} $S_n:=\sum_1^n X_k$, +\textit{or, equivalently, letting} $S_n\coloneq\sum_1^n X_k$, \[\mathbb{E} f(S_n/\sqrt{n})\to \int_{-\infty}^\infty f(t) \frac{\mathrm{e}^{-t^2/2}}{\sqrt{2\uppi}}\,\mathrm{d}t \quad\mbox{as $n\to\infty$, for every $f\in\mathrm{b} |