[[Convergence concepts in probability MOC]]
# Convergence in distribution

A sequence $(X_i)_{i=1}^\infty$ of [[Real random variable|real random variables]] is said to **converge in distribution** to a real random variable $X$ iff the [[Cumulative distribution function|CDFs]] obey #m/def/prob 
$$
\begin{align*}
\lim_{ i \to \infty } F_{X_{i}}(x) = F_{X}(x)
\end{align*}
$$
for all points where $F_{X}(x)$ is continuous.

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