Question: Let {pn}n=1 be a sequence of numbers such that 0 < pn < 1 for all n. Assume that limn pn = p with 0

Let {pn}∞n=1 be a sequence of numbers such that 0 < pn < 1 for all n. Assume that limn→∞ pn = p with 0 < p < 1. Let Xn have the binomial distribution with parameters k and pn for some positive integer k. Prove that Xn converges in distribution to the binomial distribution with parameters k and p.

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