\; \exp\left(-\frac{\left(x-\mu\right)^2}{2\sigma^2} \right) \!</math>|
The normal distribution is a probability distribution. It is also called Gaussian distribution because it was first discovered by Carl Friedrich Gauss. The normal distribution is a continuous probability distribution that is very important in many fields of science.
Normal distributions are a family of distributions of the same general form. These distributions differ in their "location" and "scale" parameters: the mean ("average") of the distribution defines its location, and the standard deviation ("variability") defines the scale. These two parameters are represented by the symbols formula_2 and formula_10, respectively.
The standard normal distribution (also known as the Z distribution) is the normal distribution with a mean of zero and a standard deviation of one (the green curves in the plots to the right). It is often called the bell curve, because the graph of its probability density looks like a bell.
Many values follow a normal distribution. This is because of the central limit theorem, which says that if an event is the sum of identical but random events, it will be normally distributed. Some examples include:
Biomass
Biomass is a basic term in ecology, and in the energy production industry.
Organic waste such as dead plant and animal material, animal dung and kitchen waste can be converted into gaseous fuel called biogas. The organic waste is decomposed by bacteria in biogas digesters to emit biogas which is essentially a mixture of methane and carbon dioxide.
In ecology, biomass means the accumulation of living matter. It is the total living material in a given area or a biological community or group. Biomass is measured by weight, or by dry weight, per given area (per square metre or square kilometer).
In the energy industry, it refers to biological material which can be used as fuel or for industrial production. Biomass includes plant matter grown for use as biofuel, and also includes plant or animal matter used for production of fibres, chemicals or heat. Biomass may also include biodegradable wastes which can be burnt as fuel. It excludes organic material which has been transformed by geological processes into substances such as coal or petroleum. It is usually measured by dry weight.
The term biomass is especially useful for plants, where some internal structures may not always be considered living tissue, such as the wood (secondary xylem) of a tree.
Biofuels include bioethanol, biodiesel & biogas.
Biomass is grown from several plants, including switchgrass, hemp, corn, poplar, willow and sugarcane. The particular plant used is usually not very important to the end products, but it does affect the processing of the raw material.
Though biomass is a renewable fuel, its use can still contribute to global warming. This happens when the natural carbon equilibrium is disturbed; for example by deforestation or urbanization of green sites.
Biomass is part of the carbon cycle. Photosynthesis converts carbon from the atmosphere into plant matter. When the plant rots or burns, the carbon goes back into the atmosphere. This happens somewhat quickly, and plant matter used as a fuel can be constantly replaced by planting for new growth. Therefore, it doesn't much change the amount of atmospheric carbon.
Although fossil fuels come from things that died long ago, they are not considered biomass by the generally accepted definition because they contain carbon that has been 'out' of the carbon cycle for a very long time. Burning fossil fuels in combustion therefore adds much carbon dioxide to the atmosphere.
Other uses of biomass, besides fuel:
Plastics from biomass, like some made to dissolve in seawater, are made the same way as petroleum-based plastics, are actually cheaper to manufacture and meet or exceed most performance standards. But they lack the water resistance of conventional plastics.
The most successful animal, in terms of biomass, is the Antarctic krill, "Euphausia superba", with a biomass of probably over 500 million tons across the world, about twice the total biomass of humans.
Biomass may also be a measure of the dried organic mass of an ecosystem.
This is a summary of biomass data.
Variance
In probability theory and statistics, the variance is a way to measure how far a set of numbers is spread out.
Variance describes how much a random variable differs from its expected value. The variance is defined as the average of the squares of the differences between the individual (observed) and the expected value. This means that it is always positive. A variance is often represented by the symbol formula_1, if the data is the entire population, and formula_2, if the data is from a sample.
In practice, variance is a measure of how much something changes. For example, temperature has more variance in Moscow than in Hawaii.
The variance is not simply the average difference from the expected value. The standard deviation, which is the square root of the variance and comes closer to the average difference, which is also not simply the average difference. Variance and standard deviation are used because it makes the mathematics easier—when adding two random variables together.
In accountancy, a variance refers to the difference between the budget for a cost, and the actual cost.
Karl Pearson, the father of biometry, first used the term variance as follows:""It is here attempted to (show) the biometrical properties of a population of a more general type that has (..) been examined, inheritance in which follows this scheme. It is hoped that in this way it will be possible to make a more exact analysis of the causes of human variability. The great body of available statistics shows us that the the deviations of a human measurement from its mean follow very closely the Normal Law of Errors, and that therefore, the variablility may be uniformly measured by the standard deviation, corresponding to the square root of the mean square error.""
Tarzan's Treehouse
Tarzan's Treehouse is a walk-through attraction in Disneyland in Anaheim, California. It was originally called the Swiss Family Treehouse. The treehouse explores the past of the Disney character Tarzan. The tree is fake, but is considered by Disney imagineers a real species or "Disneyodendron eximus" which translates to "out of the ordinary Disney tree". The tree has 1,400 branches and 300,000 polyethlyne leaves. The tree is covered in live Spanish moss.
Adam Małysz
Adam Henryk Małysz (born 3 December 1977 in Wisła, Poland) was a Polish ski jumper. He has four Olympic medals (3 silver, 1 bronze). His longest jump was 230,5 meters. Since 2011 he is a rally driver.
Salome
Salome or Salomé (Hebrew: שלומית Shlomit) (c AD 14 between 62 and 71), is the name of a character in the New Testament. Her name is not actually given there, but she was an entirely historical person. She was the daughter of Herod Antipas and Herodias. Her name is pronounced with a short 'o', and the 'e' at the end is sounded.
This Salome is not the same Salome who is said to be a witness to the Crucifixion of Jesus in Mark 15:40.
According to Mark 6:21-29, Salome was the stepdaughter of Herod Antipas, and danced before Herod and her mother Herodias at the occasion of Herod's birthday. The New Testament suggests that Salome caused John the Baptist to be executed because his spoke out that Herod's marriage to Herodias was adulterous. Herodias put her up to the demand that John be executed, something the king was initially reluctant to do.
The version in Matthew (Chapter 14, verses 311, is perhaps clearer:
Her name is established by being mentioned in the account by Flavius Josephus in Josephus's "Jewish Antiquities" (Book XVIII, Chapter 5, 4). Despite the early date of this account, she was not always called Salome until the nineteenth century, when Gustave Flaubert (following Josephus) referred to her as Salome in his play "Herodias" (1876).