All Questions

We are given $m$ balls and $n$ bins, with $m \ge n$. Each bin can contain at most $c$ balls (we assume that $c$ is an even integer). In a sequential fashion, at each time step, one ball is placed into ...

Suppose that there is an urn containing $n$ different coupons, from which $m$ coupons are being collected, equally likely, with replacement. Let $C(m)$ be the whole set of the $m$ collected coupons. ...

I am interested in the following problem: Consider a rank-3 symmetric tensor $\boldsymbol{\sigma}$ with $\sigma_{ijk}$ where $\sigma_{ijk}$ can be 0 or 1, and the symmetry is with respect to any ...

Suppose that for some $p \in \left(0, 1\right)$ and some $n \in \mathbb{N}$, we have $n$ independent Bernoulli random variables, $X_{1}, X_{2}, \dots, X_{n}$, each with mean $p$. We shall call $X_{1}, ...

Hi, I am stuck at following problem in my research. Suppose that $M=m$ is a random variable with binomial distribution with parameters $n,p$. The constants $r$ and $\gamma$ are greater than zero. $\...