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The simplest case of a normal distribution is known as the standard normal distribution or unit normal distribution. This is a special case when μ = 0 {\textstyle \mu =0} and σ 2 = 1 {\textstyle \sigma ^{2}=1} , and it is described by this probability density function (or density): φ ( z ) = e − z 2 2 2 π . {\displaystyle \varphi (z ...
Since only 0.5 mol of H 2 SO 4 are needed to neutralize 1 mol of OH −, the equivalence factor is: If the concentration of a sulfuric acid solution is c (H 2 SO 4) = 1 mol/L, then its normality is 2 N. It can also be called a "2 normal" solution. Similarly, for a solution with c (H 3 PO 4) = 1 mol/L, the normality is 3 N because phosphoric ...
The area density (also known as areal density, surface density, superficial density, areic density, mass thickness, column density, or density thickness) of a two-dimensional object is calculated as the mass per unit area. The SI derived unit is the " kilogram per square metre " (kg·m −2). In the paper and fabric industries, it is called ...
The multivariate normal distribution is said to be "non-degenerate" when the symmetric covariance matrix is positive definite. In this case the distribution has density [5] where is a real k -dimensional column vector and is the determinant of , also known as the generalized variance.
In chemistry, the mass concentration ρi (or γi) is defined as the mass of a constituent mi divided by the volume of the mixture V. [1] For a pure chemical the mass concentration equals its density (mass divided by volume); thus the mass concentration of a component in a mixture can be called the density of a component in a mixture.
Normalizing constant. In probability theory, a normalizing constant or normalizing factor is used to reduce any probability function to a probability density function with total probability of one. For example, a Gaussian function can be normalized into a probability density function, which gives the standard normal distribution.
Then, the distribution of the random variable. is called the log-normal distribution with parameters and . These are the expected value (or mean) and standard deviation of the variable's natural logarithm, not the expectation and standard deviation of itself. Relation between normal and log-normal distribution.
Unlike a probability, a probability density function can take on values greater than one; for example, the continuous uniform distribution on the interval [0, 1/2] has probability density f(x) = 2 for 0 ≤ x ≤ 1/2 and f(x) = 0 elsewhere. The standard normal distribution has probability density. If a random variable X is given and its ...