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Density (volumetric mass density or specific mass) is a substance's mass per unit of volume.The symbol most often used for density is ρ (the lower case Greek letter rho), although the Latin letter D can also be used.
The general form of its probability density function is [2] [3] = (). The parameter μ {\displaystyle \mu } is the mean or expectation of the distribution (and also its median and mode ), while the parameter σ 2 {\textstyle \sigma ^{2}} is the variance .
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols are needed for ...
The number density (symbol: n or ρ N) is an intensive quantity used to describe the degree of concentration of countable objects (particles, molecules, phonons, cells, galaxies, etc.) in physical space: three-dimensional volumetric number density, two-dimensional areal number density, or one-dimensional linear number density.
[2] [3] Probability density is the probability per unit length, in other words, while the absolute likelihood for a continuous random variable to take on any particular value is 0 (since there is an infinite set of possible values to begin with), the value of the PDF at two different samples can be used to infer, in any particular draw of the ...
Any probability density function integrates to , so the probability density function of the continuous uniform distribution is graphically portrayed as a rectangle where is the base length and is the height. As the base length increases, the height (the density at any particular value within the distribution boundaries) decreases.
Greek letters are used in mathematics, science, engineering, and other areas where mathematical notation is used as symbols for constants, special functions, and also conventionally for variables representing certain quantities. In these contexts, the capital letters and the small letters represent distinct and unrelated entities.
This integral is 1 if and only if = (the normalizing constant), and in this case the Gaussian is the probability density function of a normally distributed random variable with expected value μ = b and variance σ 2 = c 2: = (()).