We show that a single binomial observation carries absolutely no evidential value for discriminating the null hypothesis θ = 1/2 from a broad class of alternative hypotheses that allow θ to be between 0 and 1. In contrast, interval estimation methods suggest that a single binomial observation does provide some evidence against the null hypothesis. The resolution of this paradox requires the ins...

Here is the gist of the Eisenbud–Sturmfels paper Binomial ideals, Duke Math. J. 84 (1996), 1–45. The main results are that the associated primes, the primary components, and the radical of a binomial ideal in a polynomial ring are binomial if the base ring is algebraically closed. Throughout, R = k[X1, . . . , Xn], where k is a field and X1, . . . , Xn are variables over k. A monomial is an ele...

For >40 years, geneticists and science historians have appealed to the tetrad-pollen model as an explanation of the bias toward expectation in Mendel's data, albeit without experimental support. Our experiments demonstrate that pollen sampling during self-pollination in pea conforms to the binomial distribution with no evidence of a tetrad-pollen effect.

Tuenter considered centered binomial sums of the form Sr(n) = 2n ∑

In this paper we are concerned with a general class of positive linear operators of discrete type. Based on the results of the weakly Picard operators theory our aim is to study the convergence of the iterates of the defined operators and some approximation properties of our class as well. Some special cases in connection with binomial type operators are also revealed.

The binomial distribution is a well known approximation to the distance spectra of many classes of codes. We derive a lower estimate for the deviation from the binomial approximation.