Related papers: A lower bound on the probability that a binomial r…

We give the proof of a tight lower bound on the probability that a binomial random variable exceeds its expected value. The inequality plays an important role in a variety of contexts, including the analysis of relative deviation bounds in…

We derive upper bounds on the tail conditional expectation of binomial and Poisson random variables. Those upper bounds are subsequently employed to the problem of obtaining non-asymptotic lower bounds on the probability that the…

We give an elementary proof of the fact that a binomial random variable $X$ with parameters $n$ and $0.29/n \le p < 1$ with probability at least $1/4$ strictly exceeds its expectation. We also show that for $1/n \le p < 1 - 1/n$, $X$…

Let $X$ be a random variable distributed according to the binomial distribution with parameters $n$ and $p$. It is shown that $P(X>EX)\ge1/4$ if $1>p\ge c/n$, where $c:=\ln(4/3)$, the best possible constant factor.

In this paper a numerical method is presented, which finds a lower bound for the mutual information between a binary and an arbitrary finite random variable with joint distributions that have a variational distance not greater than a known…

We consider upper exponential bounds for the probability of the event that an absolute deviation of sample mean from mathematical expectation p is bigger comparing with some ordered level epsilon. These bounds include 2 coefficients {alpha,…

In this paper we derive sharp lower and upper bounds for the covariance of two bounded random variables when knowledge about their expected values, variances or both is available. When only the expected values are known, our result can be…

We provide finite sample upper and lower bounds on the Binomial tail probability which are a direct application of Sanov's theorem. We then use these to obtain high probability upper and lower bounds on the minimum of i.i.d. Binomial random…

We derive simple but nearly tight upper and lower bounds for the binomial lower tail probability (with straightforward generalization to the upper tail probability) that apply to the whole parameter regime. These bounds are easy to compute…

This paper addresses the problem of deciding the lower-boundedness of an arbitrary real polynomial p in n variables.

This paper develops upper and lower bounds for the probability of Boolean expressions by treating multiple occurrences of variables as independent and assigning them new individual probabilities. Our technique generalizes and extends the…

The exact lower bound on the probability of the occurrence of exactly one of $n$ random events each of probability $p$ is obtained.

We study the problem of computing the tightest upper and lower bounds on the probability that the sum of $n$ dependent Bernoulli random variables exceeds an integer $k$. Under knowledge of all pairs of bivariate distributions denoted by a…

We present a new proof rule for verifying lower bounds on quantities of probabilistic programs. Our proof rule is not confined to almost-surely terminating programs -- as is the case for existing rules -- and can be used to establish…

The Chernoff bound is a well-known tool for obtaining a high probability bound on the expectation of a Bernoulli random variable in terms of its sample average. This bound is commonly used in statistical learning theory to upper bound the…

We present a new positive lower bound for the minimum value taken by a polynomial P with integer coefficients in k variables over the standard simplex of R^k, assuming that P is positive on the simplex. This bound depends only on the number…

A novel, non-trivial, probabilistic upper bound on the entropy of an unknown one-dimensional distribution, given the support of the distribution and a sample from that distribution, is presented. No knowledge beyond the support of the…

In this note we prove bounds on the upper and lower probability tails of sums of independent geometric or exponentially distributed random variables. We also prove negative results showing that our established tail bounds are asymptotically…

The estimation of a probability p from repeated Bernoulli trials is considered in this paper. A sequential approach is followed, using a simple stopping rule. A closed-form expression and an upper bound are obtained for the mean absolute…

Chebyshev's inequality provides an upper bound on the tail probability of a random variable based on its mean and variance. While tight, the inequality has been criticized for only being attained by pathological distributions that abuse the…