# Questions tagged [pr.probability]

Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.

5,175 questions
25 views

38 views

123 views

### lower bound the probability of at least L collisions

Lets say we get a list $M$ containing $|M|=\sqrt{L\cdot N}$ randomly and independtly drawn elements from a set of size $N$. And lets denote the $i$-th element of the list $M$ by $M[i]$. If we now ask ...
96 views

279 views

### The probability density function of the number of coins to first fill one box of $N$

Given $N$ boxes with the same capacity $C$, I toss coins into the boxes uniformly, one by one. When any one of the boxes is full, the sum of the coins in all boxes is denoted $S$. How to compute the ...
Suppose I collect $2n$ independent samples of a probability density function $f$, which are separated into pairs $\{X_i^1, X_i^2\}$ for $1\leq i\leq n$. Suppose I now consider the set of all $2^n$ ...
given dynamic system $(X, \mathcal{B}, F, \mu), \mu \circ F^{-1}=\mu, F$ is mixing, $A \in \mathcal{B}, s.t. \mu(A) >0$. consider dynamic system \$(X\times X, \mathcal{B}\otimes \mathcal{B}, ...