<Convergence in distribution> means that the <cumulative distribution functions> satisfy
$$
\mathbb P(X_n\leq x)\longrightarrow\mathbb P(X\leq x)
$$
at every $x$ where the <cumulative distribution function> of $X$ is <continuous>. Values at its discontinuities need not converge. This definition uses only the <probability distributions>, so the <random variables> need not be defined on the same <probability space>.

Solution

Past exam of the probability course of the University of Oxford / 2014 / 1 / a / i / Solution

 Solution (source code)