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In electromagnetism, the magnetic susceptibility (from Latin susceptibilis 'receptive'; denoted χ, chi) is a measure of how much a material will become magnetized in an applied magnetic field. It is the ratio of magnetization M (magnetic moment per unit volume) to the applied magnetic field intensity H.
The chi-squared distribution is obtained as the sum of the squares of k independent, zero-mean, unit-variance Gaussian random variables. Generalizations of this distribution can be obtained by summing the squares of other types of Gaussian random variables.
The chi distribution. The noncentral chi distribution; The chi-squared distribution, which is the sum of the squares of n independent Gaussian random variables. It is a special case of the Gamma distribution, and it is used in goodness-of-fit tests in statistics. The inverse-chi-squared distribution; The noncentral chi-squared distribution
The chi distribution has one positive integer parameter , which specifies the degrees of freedom (i.e. the number of random variables ). The most familiar examples are the Rayleigh distribution (chi distribution with two degrees of freedom ) and the Maxwell–Boltzmann distribution of the molecular speeds in an ideal gas (chi distribution with ...
In the People's Republic of China, since 1984, the chi has been defined as exactly 1/3 of a metre, i.e., 33 + 1 ⁄ 3 cm (13.1 in). However, in the Hong Kong SAR the corresponding unit, pronounced tsek (cek3) in Cantonese, is defined as exactly 0.371475 m (1 ft 2.6250 in) or 1 7/32 ft. [2] The two units are sometimes referred to in English as "Chinese foot" and "Hong Kong foot".
The chi-square distribution has (k − c) degrees of freedom, where k is the number of non-empty bins and c is the number of estimated parameters (including location and scale parameters and shape parameters) for the distribution plus one. For example, for a 3-parameter Weibull distribution, c = 4.
From this representation, the noncentral chi-squared distribution is seen to be a Poisson-weighted mixture of central chi-squared distributions. Suppose that a random variable J has a Poisson distribution with mean λ / 2 {\displaystyle \lambda /2} , and the conditional distribution of Z given J = i is chi-squared with k + 2 i degrees of freedom.
The chi-squared test, when used with the standard approximation that a chi-squared distribution is applicable, has the following assumptions: [7] Simple random sample The sample data is a random sampling from a fixed distribution or population where every collection of members of the population of the given sample size has an equal probability ...