4/7/2013
The Central Limit Theorem
In the practice of statistics, most problems involving a significance test (z or t test), finding a probability, or the determination of a confidence interval requires the usage of normal approximations. Most populations have roughly normal distributions that allow for a random sample to be taken and tested without caution. However, there are some populations that just don’t fit the description of “normal”. They don’t follow a precise bell curve, and the lack of normality could leave a statistician wondering how they could possibly determine if normal approximations are appropriate. It is at this point that one of the most important theorems in statistical mathematics comes into play. The Central Limit Theorem, which was first introduced by Pierre-Simon Laplace in the late 18th century, states that as long as other important conditions are satisfied, a sample will become more normal as its size increases. An example of this is shown below. [pic]

As you can see, as “N” increased, the distribution began to appear more like a bell curve, which is just another way of saying “normal”.
Some rules have been applied to the Central Limit Theorem throughout its history that have contributed to it becoming one of the most consistently accurate mathematical theorems. For example, there are the previously mentioned ‘conditions’ that need to be met. In order to utilize the theorem, the sample must be taken randomly, pulled from the population, and it must show independence. The basic way to determine independence is through the 10% condition, which says that a sample is independent if it makes up less than 10% of the overall population. There is also the issue of deciding just how “large” the sample must be in order to be considered “large” enough to assume normality. For the most part, as long as the sample size (N) is greater than 30, the Central Limit Theorem can be applied. If N is between 10...

...central
The CentralLimitTheorem
A long standing problem of probability theory has been to find necessary and sufficient conditions for approximation of laws of sums of random variables. Then came Chebysheve, Liapounov and Markov and they came up with the centrallimittheorem. The centrallimittheorem allows you to measure the variability in your...

...CENTRALLIMITTHEOREM
There are many situations in business where populations are distributed normally; however, this is not always the case. Some examples of distributions that aren’t normal are incomes in a region that are skewed to one side and if you need to are looking at people’s ages but need to break them down to for men and women. We need a way to look at the frequency distributions of these examples. We can find them by using the...

...Serikbay Bagdat Serikbay 1
Moldir Oskenbay
English group 110
History of Kazakhstan
24 september 2014
Geography of central Asia 24.09.2014
Central Asia is the core region of the Asian continent and stretches from the Caspian Sea in the west to China in the east and from Afghanistan in the south to Russia in the north. It is also sometimes referred to as Middle Asia, and, colloquially, "the 'stans" (as the six countries generally...

...(2010) 14: 157–187 doi: 10.1093/rof/rfp018 Advance Access publication: 4 October 2009
The Limits of the Limits of Arbitrage
ALON BRAV1 , J.B. HEATON2 and SI LI3
Professor of Finance, Duke University Fuqua School of Business; 2 Partner, Bartlit Beck Herman Palenchar & Scott LLP; 3 Assistant Professor of Finance, Wilfrid Laurier University School of Business and Economics Abstract. We test the limits of arbitrage argument for the survival of...

...Richard C. Carrier, Ph.D.
“Bayes’ Theorem for Beginners: Formal Logic and Its Relevance to Historical Method — Adjunct Materials and Tutorial”
The Jesus Project Inaugural Conference “Sources of the Jesus Tradition: An Inquiry”
5-7 December 2008 (Amherst, NY)
Table of Contents for Enclosed Document
Handout Accompanying Oral Presentation of December 5...................................pp. 2-5 Adjunct Document Expanding on Oral...

...A Friend in Need is a Friend indeed Essay
There is nothing better than surrounded by good friends. You may look at some people and their friends with envy as they chat away happily and participate in activities together. It may be hard to figure out which friends are better when considering the friends who can have fun with and the friends that can get help from. From my perspective, the people who are willing to help me in the crisis time are much more cherished than who just want to stay...

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Pythagorean Theorem
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a relation in Euclidean geometry among the three sides of a right triangle (right-angled triangle). In terms of areas, it states:
In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two...

...bernoulli's theorem
ABSTRACT / SUMMARY
The main purpose of this experiment is to investigate the validity of the Bernoulli equation when applied to the steady flow of water in a tape red duct and to measure the flow rate and both static and total pressure heads in a rigid convergent/divergent tube of known geometry for a range of steady flow rates. The apparatus used is Bernoulli’s Theorem Demonstration Apparatus, F1-15. In this experiment, the pressure...