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Inferential Statisticshard
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In the context of the Bahadur-Rao theorem for large deviations, what is the asymptotic behavior of the tail probability P(Sn≥na)P(S_n \geq na)P(Sn​≥na) where Sn=∑i=1nXiS_n = \sum_{i=1}^n X_iSn​=∑i=1n​Xi​ and E[X1]=μ<aE[X_1] = \mu < aE[X1​]=μ<a?