Tight Lower Bound on the Probability of a Binomial Exceeding its Expectation
نویسندگان
چکیده
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 learning theory and generalization bounds for unbounded loss functions.
منابع مشابه
A bound for Feichtinger conjecture
In this paper, using the discrete Fourier transform in the finite-dimensional Hilbert space C^n, a class of nonRieszable equal norm tight frames is introduced and using this class, a bound for Fiechtinger Conjecture is presented. By the Fiechtinger Conjecture that has been proved recently, for given A,C>0 there exists a universal constant delta>0 independent of $n$ such that every C-equal...
متن کاملScratching the Surface of Probability
Scratch cards are widely used to promote the interests of charities and commercial concerns. They provide a useful mechanism for introducing many key concepts typically met by students in a first or second level under-graduate course involving probability modelling. The work described here stems from a real marketing problem. Simple card layouts lead quickly to consideration of combinatorial co...
متن کاملAn Elementary Analysis of the Probability That a Binomial Random Variable Exceeds Its Expectation
We give an elementary proof of the fact that a binomial random variable X with parameters n and 0.29/n ≤ p < 1 with probability at least 1/4 strictly exceeds its expectation. We also show that for 1/n ≤ p < 1 − 1/n, X exceeds its expectation by more than one with probability at least 0.0370. Both probabilities approach 1/2 when np and n(1− p) tend to infinity.
متن کاملOn Lower Bounds for the Redundancy of Optimal Codes
The problem of providing bounds on the redundancy of an optimal code for a discrete memoryless source in terms of the probability distribution of the source, has been extensively studied in the literature. The attention has mainly focused on binary codes for the case when the most or the least likely source letter probabilities are known. In this paper we analyze the relationships among tight l...
متن کاملOn monotonicity of expected values of some run-related distributions
We prove that the expectation of the binomial distribution of order k with success probability p is monotonically increasing with respect to p for all n and k. The result is extended to the problems on exchangeable random sequences and expectations of distributions of mixtures of binomial distributions of order k are studied. If the mixing measure is stochastically increasing with respect to it...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1306.1433 شماره
صفحات -
تاریخ انتشار 2013