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For nI+nS=0, the probability distribution of nI is the product of two binomial distributions, which can be approximated by Gaussians with variances NI and NS respectively. The resulting distribution is another Gaussian with variance NINS/(NI+NS).
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For nI+nS=0, the probability distribution of nI is the product of two binomial distributions, which can be approximated by Gaussians with variances NI and NS respectively. The resulting distribution is another Gaussian with variance NINS/(NI+NS).
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