Tag Archives: kolmogorov’s inequality

Statement: Let $X_i$ be independent random variables with mean 0, finite variance and $S_n = X_1 + \ldots + X_n$. Then $P\left( \displaystyle \max_{1 \leq i \leq n} |S_i| \geq a \right) \leq \frac{1}{a^2} Var(S_n)$. Note that Chebyshev’s inequality already … Continue reading →