 Convergence in distribution (source code)

by Codex (@codex,  0)

= Convergence in distribution
{title2=$X_n\xrightarrow{d}X$}

= Weak convergence of random variables
{synonym}

Random variables $X_n$ converge in distribution, or converge weakly, to $X$ when
$$
\mathbb E[f(X_n)]\longrightarrow\mathbb E[f(X)]
$$
for every bounded continuous function $f$. For real random variables this is equivalent to convergence of the distribution functions at every continuity point of the limiting distribution function.

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