The Gaussian distribution—a function that tells the probability that any real observation will fall between any two real limits or real numbers, as the curve approaches zero on either side. It is a very commonly occurring continuous probability distribution. In theory, Gaussian distributions are extremely important in statistics and are often used in the natural and social sciences for real-valued random variables whose distributions are not known. Gaussian distributions are also sometimes referred as Bell curve or normal distribution.
The probability density function of a normal (or Gaussian) distribution is defined as
Where the parameters μ is the mean or expectation of the distribution σ is the Standard deviation of the distribution σ 2 is the variance of the distribution.
And is represented as
The normal distribution is very utilizable because of the central limit theorem, which states that, under mild conditions, the mean of many arbitrary variables independently drawn from the same distribution is distributed approximately customarily, irrespective of the form of the pristine distribution: physical quantities that are expected to be the sum of many independent processes (such as quantification errors) often have a distribution very proximate to the Gaussian. Moreover, many results and methods (such as propagation of dubiousness and least squares parameter fitting) can be derived analytically in explicit form when the germane variables are normally distributed.
Normal distribution curves are symmetrical about the mean and the curve has some o special properties like:
1) The mean, median and mode are equal.
2) Graph is symmetrical about the mean.
3) The two ends are asymptotic to horizontal ...
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...ghly mundane distributions, with few members at the high and low ends and many in the middle.
Because they occur so frequently, there is an infelicitous propensity to invoke mundane distributions in situations where they may not be applicable. As Lippmann verbally expressed, "Everybody believes in the exponential law of errors: the experimenters, because they cerebrate it can be proved by mathematics; and the mathematicians, because they believe it has been established by observation"
Among the astounding properties of the mundane distribution are that the mundane sum distribution and mundane difference distribution obtained by respectively integrating and subtracting varieties X and Y from two independent mundane distributions with arbitrary betokens and variances are additionally mundane! The mundane ratio distribution obtained from X/Y has a Cauchy distribution.
(http://www.encyclopedia.com/doc/1O7-densityfrequencydominance.html) Biodiversity is the number of richness or the number of species in a local area. This happens when someone can look at a species, in order to indicate a degree of uncertainty. This can happen by calculating the number of species given, where the individual is picked at random from the community. In other words, if the diversity is high, then oneself will have a poorer chance of correctly calculating the species of the next individual picked at random. (http://www.tiem.utk.edu/~gross/bioed/bealsmodules/shannonDI.html) This experiment was a way to find out the diversity of the school parking lot and the possibility to identify the type or model of the student’s, faculties and guest
The premise of this argument is that "At times it 's simply because of human error" with the conclusions being that "It goes on all the time" and "it 's not easy to stop".
Physiologic density- is the number of people per unit area of arable land which is land suitable for agriculture (farmable land).
Introduction to the basic concepts of probability and statistics with discussion of applications to computer science.
Normal yield curve – it is an upward slope yield curve in which short-term securities have lower yield than long-term securities. As the name suggested, the shape essentially indicate the normal condition in the market where investors believe that there will be no significant changes in the economy such as that the economy will develop at a normal rate. It is actually a normal expectation of the market to offer higher yield to long-term security as compensation because they hold more risk than the short-term security.
A trend line is a straight line drawn through the center of a group of points plotted on a scatter plot.
what is normal and usual; that it is not usual to be able to describe
Prior to the winding-up of an insolvent company, its creditors may individually enforce any measure available to them in order to obtain payment of the debt owed to them by such company. However, upon the opening of the winding-up proceedings these individual actions are replaced by a collective insolvency regime which attempts to ensure the rateable and equitable distribution of the assets of the insolvent company among its creditors. This distribution is known as pari passu distribution.
A number of variability may increase in how big is the specie and how are they distributed.
The extent to which a distribution of values deviates from symmetry around the mean is the skewness. A value of zero means the distribution is symmetric, while a positive skewness indicates a greater number of smaller values, and a negative value indicates a greater number of larger values (Grad pad, 2013). Values for acceptability for psychometric purposes (+/-1 to +/-2) are the same as with kurtosis.
...en Goldachre. (2011). The statistical error that just keeps on coming. Available: http://www.guardian.co.uk/. Last accessed 10/12/2011.
Statistics work for everything when there is a lot of it. They work for money, molecules, atoms, star systems, and even people. People tend to adhere to statistics when there is a fair amount of people to stifle the occasional fluctuations in human behavior. Many things we do depend on statistics. Take war for example. War is a very good example, since the outcome depends more on the general strategy of the whole war, than on individual soldiers. It follows definite rules that can be expressed in formulas. The individual people in war tend to become statistics, in the eyes of the high command, the public, as well as in their own perception. Tim O’Brien wonderfully illustrates this in his essay “How to Tell a True War Story.” He relates that there is no point to any events or actions according to the perception of the soldier during a war. “You smile and think, ... what’s the point?” (469) he says. A person then becomes nothing more than a statistic -- a part of a whole behaving in a random way. If there is no point to existence, then his actions are truly random. Something truly random can be easily studied, stimulated, expressed in some numbers, percentages, probabilities. This randomness of the soldier is what the whole military apparatus depends on. Consider: if the life of a soldier during war had a point, if he realized that there is some underlying meaning, wouldn’t he strive toward the goal assigned by that meaning? He would, for that is in human nature. Now, if there was no meaning in his perception, he could easily be persuaded that a particular thing must be done. He will obediently follow.
Data is collected and the patterns are recognized, in order to understand the physical properties, and further to visualize the data as
Often uses random sampling to select a large statistically representative sample from which generalizations can be drawn.
...Gauss was an incredible mathematician that founded ideas in the fields of geometry, statistics, number theory, statistics, and more. He was able to change the attitudes of mathematicians everywhere with his curious, but brilliant and logical mind and find solutions to problems they have had for hundreds of years. His work is so important and useful that it is still used today in math fields and classes everywhere. The inclusion of Gauss in the history of mathematics is an important one and without his exceptional mind modern day math would be almost entirely different than it is.