Strengthening the teaching of probability requires an adequate training prospective teachers, which should be based on prior assessment their knowledge. Consequently, aim this study was to analyse how 139 Spanish mathematics teachers relate classical and frequentist approaches probability. To achieve goal, content analysis used categorize teachers’ answers a questionnaire with open-ended tasks ...

The list of physically motivated urn models that can be solved in terms classical orthogonal polynomials is very small. It includes a model proposed by D. Bernoulli and further analyzed S. Laplace P. T. Ehrenfest eventually connected with the Krawtchouk Hahn polynomials. This connection was reversed recently case Jacobi where rather contrived, later simpler proposed. Here we consider an going J...

The Pólya process is an urn scheme arising in the context of the contagion spreading. It exhibits unstable persistence effects. The Friedman urn process is dual to the Pólya one with antipersistent stabilizing effects. It appears in a safety campaign problem. A Pólya-Friedman urn process is investigated with a tuning persistence parameter extrapolating the latter two extreme processes. The stud...

This study investigates the effects of grid resolution on hydroacoustic performance benchmark INSEAN E779A propeller operated in uniform flow, open water and non-cavitating conditions. In numerical calculations, an incompressible hydrodynamic solver together with porous FW-H (Ffowcs-Williams Hawkings) equation is used to predict URN (Underwater Radiated Noise). The first aim within this explore...

SUMMARY An urn model of Diaconis and some generalizations are discussed. A convergence theorem is proved that implies for Diaconis' model that the empirical distribution of balls in the urn converges with probability one to the uniform distribution.

We prove a Central Limit Theorem for the sequence of random compositions of a two-color randomly reinforced urn. As a consequence, we are able to show that the distribution of the urn limit composition has no point masses.

In this article we review the important statistical properties of the urn randomization (design) for assigning patients to treatment groups in a clinical trial. The urn design is the most widely studied member of the family of adaptive biased-coin designs. Such designs are a compromise between designs that yield perfect balance in treatment assignments and complete randomization which eliminate...

We propose a segmentation method based on Polya's (1931) urn model for contagious phenomena. A preliminary segmentation yields the initial composition of an urn representing the pixel. The resulting urns are then subjected to a modified urn sampling scheme mimicking the development of an infection to yield a segmentation of the image into homogeneous regions. This process is implemented using c...

We consider a generalized form of the coupon collection problem in which a random number, S, of balls is drawn at each stage from an urn initially containing n white balls (coupons). Each white ball drawn is colored red and returned to the urn; red balls drawn are simply returned to the urn. The question considered is then: how many white balls (uncollected coupons) remain in the urn after the ...