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In probability and statistics, a probability distribution assigns a probability to each measurable subset of the possible outcomes of a random experiment, survey, or procedure of statistical inference.
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Kolmogorov inequality for Bernoulli random variables
This question is also asked on math stackexchange. The question is about one inequality which shows in Kolmogorov's paper (inequality (3.1)) but is not proved. The inequality says that, if we assume $ …
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A functional equation coming from a distribution function
Currently, I am working on a random series as follows. Let $\{Y_k\}$ be a sequence of i.i.d. Bernoulli random variables with expectation $p$. Then we define
$$
S = \sum_{k=1}^\infty \prod_{\ell=1}^k 2 …