Narrow Results

The following sections are included:

• INTRODUCTION

• RANDOM EXPERIMENT, OUTCOMES, SAMPLE SPACE, EVENT, AND PROBABILITY
  • Properties of Random Experiments
  • Sample Space of an Experiment and the Venn Diagram
  • Probabilities of Outcomes
  • Subjective Probability

• ALTERNATIVE EVENTS AND THEIR PROBABILITIES
  • Probabilities of Union and Intersection of Events
  • Partitions, Complements, and Probability of Complements
  • Using Combinatorial Mathematics to Determine the Number of Simple Events

• CONDITIONAL PROBABILITY AND ITS IMPLICATIONS
  • Basic Concept of Conditional Probability
  • Multiplication Rule of Probability

• JOINT PROBABILITY AND MARGINAL PROBABILITY
  • Joint Probability
  • Marginal Probabilities

• INDEPENDENT, DEPENDENT, AND MUTUALLY EXCLUSIVE EVENTS

• BAYES’ THEOREM

• BUSINESS APPLICATIONS
  • Determination of the Commercial Lending Rate
  • Analysis of a Personnel Data File
  • Soda Purchase Survey
  • Ages and Years of Teaching Experience

• Summary

• Appendix 5A Permutations and Combinations
  • Permutations
  • Combinations
  • Outcome Trees and Probabilities

• Questions and Problems

Probability theory is the foundation of statistical science, providing a mathematical means of modeling random experiments or uncertainty. Through these mathematical models, researchers are able to draw inferences about the random experiments using observed data. The aim of this chapter is to outline the basic ideas of probability theory that are fundamental to the study of statistics. The entire structure of probability, and therefore of statistics, can be built on the relatively straightforward foundation given in this chapter.

Creating direct and dramatic visual use of the Mereon Trefoil as time and a knotted fold in space-time, the dynamics are imagined as geometric lines of force that turn the Mereon Matrix inside out. It is shown that Mereon’s toroidal dynamics are reflected in nature’s patterns and human social patterning. This chapter presents how the Matrix’s 33 planar ‘landshapes’, similar to Russian dolls, imprint the knot with particular symmetries that define the Mereon Trefoil as a knotted ‘timeshape’, all aspects time and space connected to and embedded with prior ‘time-slices’. Chirality is shown to be implicit in the knot, and us revealed to have a fundamental relationship with the smallest 3D polyhedra, two types of tetrahedron. The Mereon Trefoil is demonstrated equal to a minimal Enneper surface; all polyhedra are shown to ‘tie’ the knot, and like the geometry, the topology scales to infinity.

Octrees offer a powerful means for representing and manipulating 3-D objects. This paper presents an implementation of octree manipulations using a new approach on a shared memory architecture. Octrees are hierarchical data structures used to model 3-D objects. The manipulation of these data structures involves performing independent computations on each node of the octree. Octrees are much easier to deal with than other forms of representations used to model 3-D objects especially where extensive manipulations are involved. When these operations are distributed among multiple processing elements (PEs) and executed simultaneously, a significant speedup may be achieved. Manipulations such as a complement, a union, an intersection and other operations such as finding the volume and centroid which this paper describes are implemented on the Sequent Balance multiprocessor, hi this approach the PEs are allocated dynamically, resulting in a uniform load balancing among them. The experimental results presented illustrate the feasibility of the approach. Although this evaluation has been originally done for shared memory machines, it will provide insight for the evaluation of other architectures.

In the urban road network, urban road intersection is a major bottleneck in the urban road network capacity and traffic capacity. Ensure the orderly and smooth running of urban road intersections, and to improve urban traffic conditions is important. Nongye Lu and Wenhua Lu intersection as the two main roads cross the intersection, Zhengzhou, congestion is very serious.

Over the years, there has been the intersection traffic congestion problems, delay time and serious environment pollution etc.. In order to ease the traffic tension, improve the efficiency of road and facilitate travel, it is necessary to spend time and effort to study the intersection. This paper takes the city road intersection as the breakthrough point, through field survey, through the relevant calculation, idea and scheme is proposed to improve the hardware facilities, bypass shunt. In order to solve the congestion problem in the intersection.