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In class, I was shown that the Binomial prob density function converges to the Poisson prob density function. But why does this show that the Binomial distribution converges in distribution to the Poisson dist. ? Convergence in distribution requires that the cumulative density functions converges (not necessarily the prob density functions).

Is it because both are non negative and start at zero --> therefore convergence in prob. density functions implies converges in cumulative density functions?

Thank you.

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# Why does Binomial dist. converge in distribution to Poisson dist. ?

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