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Distributionshard
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Consider a sequence of i.i.d. random variables Xi∼Bernoulli(p)X_i \sim \text{Bernoulli}(p)Xi​∼Bernoulli(p). Let Yn=∑i=1nXiY_n = \sum_{i=1}^n X_iYn​=∑i=1n​Xi​. For a fixed nnn and large ppp, which distribution serves as the best approximation for the distribution of YnY_nYn​ if we center and scale it appropriately?