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Proof of convergence in distribution of a discrete random variable
I'm working on a question on "convergence in distribution" and I appreciate if you could guide me on how to approach this question:
Here is the question:
Let $X_n$ be integer-valued random variables. Show that $X_n \rightarrow^w X_{\infty}$ converges in distribution if and only if $\mathrm{Pr}(X_n = m) \rightarrow \mathrm{Pr}(X_{\infty} = m)$ for each $m$.
I appreciate your help.