Abstract
This paper describes the binomial theorem, which is based on the idea of expanding powers of sum. According to the paper, it provides an easy way to methodologically expand terms that are summed or raised to a power. The binomial theorem can be used for all real or complex numbers x and y. The paper concludes by noting that there exists a pattern to this expansion, despite the appearance that the binomial theorem seems like a trivial calculation.

From the Paper
"The binomial theorem is based on the idea of expanding powers of sum. It is very important and very popular and provides an easy way to methodologically expand terms that are summed or raised to a power. For example, the most popular expansion is the square of a sum, given by: (x+y)^2 = x^2+2xy+y^2...................Equation 1 Equation 1 shows how to expand the squared sum of two terms, and shows the value of each term after expansion. The binomial can be used for any number of powers needed for expanding the sum, in fact the general version of the binomial formula is..."

Tags:binomial, roles, pascal

Abstract
This paper contains the answers to twenty five questions that deal with probability and systems engineering. Poisson, normal, binomial, and exponential distributions are among the topics covered. In addition, parallel systems with respect to failures and safety are discussed. Some problems are explained with respect to finding the occurrence or probability.

From the Paper
1. The complementary law of probability states that if A is an event, then the complement of A, denoted by A"a' , represents the event composed of all basic outcomes in S (a set, group, or area) that do not belong to A. The formula or calculation for this law is P(A"a' ) = 1 - P(A). 2. Inspecting 5 sensors randomly - probability of finding one that is failed if 3 have failed is as follows - there are 3/5 sensors that are failed, therefore the probability of finding a failed sensor is 3/5 or 0.60 - a sixty percent chance of inspecting a failed sensor. Another way of stating this is through the additive law of probability since each sensor that is failed is 1/5, therefore (1/5) + (1/5) + (1/5) for each of

Tags:probability, systems, engineering

Abstract
Statistics refers to the processes of collecting, organizing, analyzing and presenting data in forms usable for policy analysis, decision-making and other important tasks confronting people and organizations in contemporary society. It is within this framework that Polk Company, one of America's oldest and largest consumer marketing firms, operates.
This study considers the application at the Polk Company of 11 tasks associated with the processes of collecting, organizing, analyzing and presenting data. In each instance, the data management or statistical analysis function is defined, the learning process is explained within the context of the Kolb Model, and an illustration of the application of the data management or statistical analysis function is presented. The 11 data management or statistical analysis functions are (1) organizing data, (2) averages and variations, (3) elementary probability theory, (4) normal distribution, (5) binomial distribution, (6) sampling distribution, (7) estimation, (8) hypothesis testing, (9) regression and correlation, (10) chi square and analysis of variance (ANOVA) which is based on the F statistic and (11) non-parametric statistics.

From the Paper
"Type 1 learners, when working with hypotheses, tend to review available data without bias and study and consider the data from a variety of perspectives to develop workable hypotheses related to analytical objectives. Type 2 learners would approach the task by developing theoretical models upon which to base hypotheses, and then study and consider the data from a variety of perspectives in which model best supports the development of workable hypotheses. Type 3 learners would approach the task by developing theoretical models upon which to base hypotheses, and then experiment with alternative hypotheses to determine how best to achieve analytical objectives. Type 4 learners would review available data without bias, and then experiment with alternative hypotheses to determine how best to achieve analytical objectives."

Tags:Quantitative, binomial

Abstract
First, the multiplication of binomials and trinomials is explained step by step in detail. Next, factoring binomials and trinomials is discussed because this is the multiplication of polynomials in reverse. Finally, trinomials and polynomials with 4 or more terms are examined in detail.

From the Paper
"This document examines and explains polynomials in algebraic expressions. First, the multiplication of binomials and trinomials is explained step by step in detail. Next, factoring binomials and trinomials is discussed because this is the multiplication of polynomials in reverse. Finally, trinomials and polynomials with 4 or more terms are examined in detail. Algebraic Polynomials Problem I: (3xy + 2x)(x2 + 2xy2) The first terms in the binomial should be multiplied: 3xy * x^2 = 3x^3y..."

Tags:algebraic, polynomials, formulas

Abstract
This paper reviews three articles that discuss some form of financial risk modeling methodology. The articles discussed are "Model-Based Stress Test: Linking Stress Tests to VaR for Market Risk" by Carol Alexander and Elizabeth Sheedy, "Risk and Probability Measures" by Phelem Boyle, and "Realized Volatility and Correlation" by Anderson, Torben, et al.


Table of Contents:
Abstract
Article Reviews
Alexander, Carol and Elizabeth Sheedy. "Model-Based Stress Test: Linking Stress Tests to VaR for Market Risk".
Boyle, Phelim. "Risk and Probability Measures."
Anderson, Torben, et al. "Realized Volatility and Correlation."

From the Paper
"Volatility is the focus of all risk modeling in financial analysis because the greater the volatility the greater the risk of the investment or a portfolio exhibiting a high degree of volatility. Anderson et al, in "Realized Volatility and Correlation" describe how volatility has come to dominate risk modeling literature and that this literature has increasingly focused on "higher-frequency data". Thus begins these researchers' quest to attempt to match actual volatility levels with more accurate forecasting techniques."

Tags:portfolio skewness methodology value-at-risk, binomial tree model

Abstract
A paper which considers how the work of Kepler, Newton, Copernicus, Brahe, Ptolemy and Galileo overlapped, how one discovery influenced another and how the work of these scientists helped form the foundation of modern scientific knowledge of the physical sciences. The paper studies the life histories of each of these scientists.

From the Paper
"Galileo was appointed professor of mathematics at Padua, his duties included to teach the geometry of Elucid, and geocentric, astronomy to the medical students. However it is noted that he discussed more natural philosophy and forms of non standard astronomy, this was also carried out in a public lecture in reference to a New Star that had appeared, now known as Kepler s supernova. Galileo also wrote personally to Kepler stating that he was a follower of the Copernican theory, however there was no outward evidence of this until many years later (Field, 1995)."

Tags:Greek, historian, Copernican, theory, planetary, motion, binomial, theorem, Kepler, Newton, Copernicus, Brahe, Ptolemy, Galileo