Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some inequalities on Binomial and Poisson probabilities   Let $S$ and $X$ be independent random variables, assuming values in the set
of non-negative integers, and suppose further that both $\mathbb{E}(S)$ and
$\mathbb{E}(X)$ are integers satisfying $\mathbb{E}(S)\ge \mathbb{E}(X)$. We
establish a sufficient condition for the tail probability $\mathbb{P}(S\ge
\mathbb{E}(S))$ to be larger than $\mathbb{P}(S+X\ge \mathbb{E}(S+X))$. We also
apply this result to sums of independent binomial and Poisson random variables.

31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg