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Distributionshard
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For a Binomial random variable X∼Binomial(n,p)X \sim \text{Binomial}(n, p)X∼Binomial(n,p), consider the sample proportion p^=X/n\hat{p} = X/np^​=X/n. What is the limiting distribution of n(p^−p)\sqrt{n}(\hat{p} - p)n​(p^​−p) as n→∞n \to \inftyn→∞?