In this note, a coin tossing experiment which leads to three discrete distributions is discussed.

The authors present a theory of stochastic interactive parallel processing with special emphasis on channel interactions and their relation to system capacity. The approach is based both on linear systems theory augmented with stochastic elements and decisional operators and on a metatheory of parallel channels' dependencies that incorporates…

Consider a trough with a uniform cross section that is bounded by different functions on its two sides, and assume that the trough can be tipped either way. The question explored is this: If the trough is partially filled with water, what angle of tipping will maximize the depth of the water?

The modular ring Z[subscript 6] defines integers via ( 6r[subscript i] + ( i - 3)) where i is the class and r[subscript i] the row when tabulated in an array. Since only Classes 2[subscipt 6] and 4[subscript 6] contain odd primes, this modular ring is ideally suited to the analysis of twin primes. The calculations are facilitated by the use of the…

In this paper, the author shows that that there are infinitely many Fermat primes of the form n[squared] + 1. Some results of his recent computations are presented. (Contains 1 figure.)

The purpose of this paper is to delineate some insights into the concept of multisets along with a couple of combinatorial results related to multisets. The paper indicates that a general formula needs to be worked out for determining the cardinality of the "Set" (whose elements may be multisets but do not repeat) of all multisubsets of a finite…

In this note, using the theory of Pell equation, the authors discuss the integrity of certain series involving generalized Fibonacci and Lucas numbers.

The problem of estimating the cross-product of two mean vectors in three-dimensional Euclidian space is considered. Two "natural" estimators are developed, both of which turn out to be biased. A third, unbiased estimator, resulting from a jackknife procedure, is also investigated. It is shown that, under normality, the latter is best among all the…

The circle discussed in this paper is named after "The Great Geometer of Antiquity", that is Apollonius of Perga (ca. 262-190 BCE). Among his many contributions to geometry is a book with the title "Plane Loci." This book included, among others, a problem about the locus of a point moving in a plane such that the ratio of its distances from two…

This paper reports on a study conducted to investigate the consistency of the results between 2 approaches to estimating school effectiveness through value-added modeling. Estimates of school effects from the layered model employing item response theory (IRT) scaled data are compared to estimates derived from a discrete growth model based on the…

The correlation between a short-form (SF) test and its full-scale (FS) counterpart is a mainstay in the evaluation of SF validity. However, in correcting for overlapping error variance in this measure, investigators have overattenuated the validity coefficient through an intuitive misapplication of P. Levy's (1967) formula. The authors of the…

This study illustrates how a diagnostic testing model can be used to make detailed comparisons between student populations participating in international assessments. The performance of Turkish students on the TIMSS-R mathematics test was reanalyzed with a diagnostic testing model called the Rule Space Model. First, mathematical and cognitive…

In this study, a cost function is used to estimate the costs for California districts to meet the achievement goals set out for them by the state. I calculate estimates of base costs (i.e., per pupil costs in a district with relatively low levels of student need) and marginal costs (i.e., the additional costs associated with specific student…

This study examined the relation between benchmark data and rate of growth across the year for reading, math computation, and math concepts and applications curriculum-based measures, and a statewide and large-scale achievement test. Results showed that reading and math benchmarks were significantly and moderately correlated with performance on…