Скачать с ютуб The Kolmogorov Maximal Inequality в хорошем качестве

The Kolmogorov Maximal Inequality

We prove the Kolmogorov Maximal Inequality: Given an sequence of independent identically distributed random variables with mean zero and finite variance, the probability that the maximum of the absolute value of any partial sum exceeding a fixed level, \lambda, is not more than the variance of the last term divided by \lambda^2. This inequality is very useful when proving results about convergence of infinite random series. #mikethemathematician, #mikedabkowski, #profdabkowski