Random definition

Random variable. A term which has been given many variable, if not entirely random, definitions. Broadly and loosely for our purposes, some measurement which takes on given values with given probabilities. 

Random definition of the first generation of catalytic materials based on the components and preparation methods selected. In order to adjust parameters concerning the catalyst composition or preparation in a meaningful way, parameters can be assigned to groups of components. 

The field that generates these eddy currents is, by its nature, anisotropic, i e the eddy current signal response is directionally dependent on probe orientation. This can be used advantageously if one bears in mind that the corroded material one aims to detect usually displays random peaks and valleys, while man-made edges have a definite orientation. 

Let a(t) denote a time dependent random process. a(t) is a random process because at time t the value of a(t) is not definitely known but is given instead by a probability distribution fimction W (a, t) where a is the value a (t) can have at time t with probability detennmed by W (a, t). W a, t) is the first of an infinite collection of distribution fimctions describing the process a(t) [7, H]. The first two are defined by... 

Uncertainty expresses the range of possible values that a measurement or result might reasonably be expected to have. Note that this definition of uncertainty is not the same as that for precision. The precision of an analysis, whether reported as a range or a standard deviation, is calculated from experimental data and provides an estimation of indeterminate error affecting measurements. Uncertainty accounts for all errors, both determinate and indeterminate, that might affect our result. Although we always try to correct determinate errors, the correction itself is subject to random effects or indeterminate errors. 

By combining random flight statistics from Chap. 1 with the statistical definition of entropy from the last section, we shall be able to develop a molecular model for the stress-strain relationship in a cross-linked network. It turns out to be more convenient to work with the ratio of stretched to unstretched lengths L/Lq than with y itself. Note the relationship between these variables ... 

Sample Statistics Many types of sample statistics will be defined. Two very special types are the sample mean, designated as X, and the sample standard deviation, designated as s. These are, by definition, random variables. Parameters like [L and O are not random variables they are fixed constants. 

Tile following properties of the cdf of a random variable X can be deduced directly from tlie definition of F(x) in Eq. (19.8.2). 

Random copolymer—Distribution of the monomer units does not follow any definite sequence. These are produced in bulk, aqueous, suspension, or emulsion using free radical initiators of the peroxide type or redox systems. 

It is important to recognize that the following analytical methods essentially determine EO-PO ratio ( H NMR, IR, cleavage methods) or even simply alkylene oxide content (compleximetric methods) of the analyte, and as such are not specific quantitative or qualitative methods for poloxamers, since EO-PO copolymers of a different structure (for instance, random copolymers, or PO-EO-PO block copolymers) may respond to the methods in a way indistinguishable from poloxamers. The principal technique that permits definitive identification of a sample as a poloxamer is C NMR, which allows structural details, such as the distribution of EO and PO units along the polymer chain, to be elucidated [10]. 

Tang Herbal, 147 Target-based drug discovery biological targets, 180-184 chemical end point in, 180 chemical tools, 178-179 definition of, 5 description of, 175-177 linear approach, 176 orphan receptors, 180 preclinical process in, 176-177 random variation in gene expression, 178... 

X-ray emission spectrography, in common with other analytical methods, is subject to errors of different kinds. Lacking better information, we shall usually assume these errors to be independent and random. (Drift caused by changes in the electronic system is definitely not random.) Before we consider errors in general, we shall examine one that is not only important and unavoidable, but that also sets x-ray... 

The quantities n, V, and (3 /m) T are thus the first five (velocity) moments of the distribution function. In the above equation, k is the Boltzmann constant the definition of temperature relates the kinetic energy associated with the random motion of the particles to kT for each degree of freedom. If an equation of state is derived using this equilibrium distribution function, by determining the pressure in the gas (see Section 1.11), then this kinetic theory definition of the temperature is seen to be the absolute temperature that appears in the ideal gas law. 

By Eq. (1-55), we have px — m Jujaf dv. Since mut is the random momentum in the -direction (. e., the momentum associated with the -component of the random velocity), the (i,j) component of the pressure tensor is the average of the random flow in the -direction of the -directed momentum. From the definition of the temperature, Eq. (1-45), the hydrostatic pressure, defined as one-third of the trace of the pressure tensor, is... 

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