# Questions tagged [probability-inequalities]

Probability Inequalities are useful for bounding quantities that might otherwise be hard to compute. A related concept is a concentration inequality, which specifically provides bounds on how far a random variable deviates from some value.

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### Chernoff Bounds for Independent Bernoulli Sums

What is wrong with this proof? Can you notice that? or I am wrong? In my opinion, in the R.H.S. of the inequality (3.2), the index of 'e' is negative but it must be positive if we use the given proof ...
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### Can positive values with sd > mean have skewness = 0?

I'm trying to create an example of a distribution with all positive values, standard deviation > mean, and skewness =0 (third moment). I cannot. Is that possible? Can you prove it mathematically? ...
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### Application of Hoeffding's inequality on the Stochastic Multi-Armed Bandit Problem

I'm following this note to learn about deriving an upper bound of the UCB algorithm on the Stochastic Multi-Armed Bandit Problem. In particular, the proof of Lemma 15.6 there connotes that we can ...
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### Game of guessing or is it! [closed]

I am trying to learn coding and want to create a simple game. The idea is that there are 20 different animals, and you have 5 rooms, each round 5 out of the 20 animals hide in the room, where behind ...
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I am stuck on the first part of problem 8.2 of the book "A Probabilistic Theory of Pattern Recognition" by Luc Devroye: Show that for any $s > 0$, and any random variable $X$ with \$\...