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In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable.The general form of its probability density function is [2] [3] = ().
The gauss is the unit of magnetic flux density B in the system of Gaussian units and is equal to Mx/cm 2 or g/Bi/s 2, while the oersted is the unit of H-field. One tesla (T) corresponds to 10 4 gauss, and one ampere (A) per metre corresponds to 4π × 10 −3 oersted .
The figure on the right was created using A = 1, x 0 = 0, y 0 = 0, σ x = σ y = 1. The volume under the Gaussian function is given by V = ∫ − ∞ ∞ ∫ − ∞ ∞ f ( x , y ) d x d y = 2 π A σ X σ Y . {\displaystyle V=\int _{-\infty }^{\infty }\int _{-\infty }^{\infty }f(x,y)\,dx\,dy=2\pi A\sigma _{X}\sigma _{Y}.}
A different technique, which goes back to Laplace (1812), [3] is the following. Let = =. Since the limits on s as y → ±∞ depend on the sign of x, it simplifies the calculation to use the fact that e −x 2 is an even function, and, therefore, the integral over all real numbers is just twice the integral from zero to infinity.
There are three parameters: the mean of the normal distribution (μ), the standard deviation of the normal distribution (σ) and the exponential decay parameter (τ = 1 / λ). The shape K = τ / σ is also sometimes used to characterise the distribution. Depending on the values of the parameters, the distribution may vary in shape from almost ...
Dihydrogen monoxide is a name for the water molecule, which comprises two hydrogen atoms and one oxygen atom (H 2 O).. The dihydrogen monoxide parody is a parody that involves referring to water by its unfamiliar chemical systematic name "dihydrogen monoxide" (DHMO, or the chemical formula H 2 O) and describing some properties of water in a particularly concerning manner — such as the ...
(), where (2n − 1)!! is the double factorial of (2n − 1), which is the product of all odd numbers up to (2n − 1). This series diverges for every finite x , and its meaning as asymptotic expansion is that for any integer N ≥ 1 one has erfc x = e − x 2 x π ∑ n = 0 N − 1 ( − 1 ) n ( 2 n − 1 ) ! !
10 −2 T centitesla 10 mT: 100 G: 30 mT: 300 G: Penny-sized ferrite magnet: 10 −1 T: decitesla: 100 mT: 1 kG: Penny-sized neodymium magnet: 150 mT: 1.5 kG: Sunspot: 10 0 T tesla 1 T: 10 kG: Inside the core of a 60 Hz power transformer (1 T to 2 T as of 2001) [10] [11] or voice coil gap of a loudspeaker magnet (1 T to 2.4 T as of 2006) [12] 1 ...