Math Solutions

Solution: Let S_n=∑_i=1^n X_i, where (X_i) are i.i.d. with exponential(1) distribution. Use the large deviation theorem to get explicit limits for

Question: Let \(S_{n}=\sum_{i=1}^{n} X_{i}\), where \(\left(X_{i}\right)\) are i.i.d. with exponential(1) distribution. Use the large deviation theorem to get explicit limits for \(n^{-1} \log P\left(n^{-1} S_{n} \geq a\right), a>1\) and \(n^{-1} \log P\left(n^{-1} S_{n} \leq a\right), a<1\)

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