The detected events thus become a point cloud data with attributed experimentally measured values, such as ion time of flight or experimentally derived quantities, e . g . time of flight or detector data.
22.
In analyzing the results of an experiment, the mean and variance of the derived quantity " z, " which will be a random variable ", " are of interest.
23.
Specifically, considering the rotation of vectors and derived quantities ( i . e ., tensors of higher order via tensor multiplication ) does not provide for all the properties of rotations as a more abstract concept.
24.
Integrating this from zero to positive infinity returns unity, which verifies that this is a PDF . Next, the mean and variance of this PDF are needed, to characterize the derived quantity " z ".
25.
Strictly speaking, the refractive index is a derived quantity telling us how the wavevector is related to the optical frequency and propagation direction of the light, thus the sign of " n " must be chosen to match the physical situation.
26.
People who want to include derived quantities like t / w could do so more justifiably in the'full spec'table . regular users wouldn't have to wade through a lot of extra techinical data if they didn't want to.
27.
Thus, even when using arguably the simplest nonlinear function, the square of a random variable, the process of finding the mean and variance of the derived quantity is difficult, and for more complicated functions it is safe to say that this process is not practical for experimental data analysis.
28.
An even bigger advantage of this formulation is, however, that it is emphasizes that " heat flow " and " power " are the basic thermodynamic properties and that heat and work are derived quantities being the time integrals of the heat flow and the power respectively.
29.
To illustrate, a simple example of this process is to find the mean and variance of the derived quantity " z = x 2 " where the measured quantity " x " is Normally distributed with mean " ? " and variance " ? 2 ".
30.
If, as is usually the case, the PDF of the derived quantity has not been found, and even if the PDFs of the measured quantities are not known, it turns out that it is still possible to estimate the mean and variance ( and, thus, the standard deviation ) of the derived quantity.
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