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Results tagged with pr.probability
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user 90197
Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
3
votes
1
answer
155
views
Expected size of the smallest preimage set
Let $f$ a function from $\{0, 1 \}^{2n}$ to $\{0, 1 \}^{n}$ uniformly picked at random. I would like to have an estimation of the expected size of the smallest premiage set of $f$, more formally $\mat …
- 215
3
votes
2
answers
478
views
Lower bound for the probability of binomial variable to be less than her expectation
Let $X$ a binomial variable of parameter $(N,p)$, with $0<p<0.5$
I would like to lower bound $\mathbb{P}\left(X <Np \right)$ by a constant ($\frac{1}{5}$ seems true and is enough for me).
Thank you b …
- 215