Solution
= Solution
<Convergence in distribution> to $Y$ means convergence of <cumulative distribution functions> at every <continuity point> of the <limiting distribution> function:
$$
\boxed{F_{Y_n}(x)\longrightarrow F_Y(x)\quad\text{whenever }F_Y\text{ is continuous at }x.}
$$
Convergence at a jump of $F_Y$ is not required. Only the laws are involved, so this definition does not require a particular <coupling> of the variables.