[[random variable|Random variables]] are said to converge in distribution when the distributions of the random variables approximate each other at the limit as n goes to infinity. We write $X_n \overset{d}{\to} X$ Formally, let $X_1, X_2, \dots, X_n$ be a sequence of random variables where $X_n$ has some [[cumulative density function|cdf]] $F_n(x) = P(X_n \le x)$ Let $X$ be a random variables with cdf $F(x) = P(X \le x)$ The sequence converges in distribution if $\lim_{n \to \infty} F_n(x) = F(x)$ at all points of continuity of $F$. Convergence in distribution is a weak form of convergence. If a random variable [[converges in probability]], it also converges in distribution. #expand The pdf of a t distribution converges to the pdf of a standard normal