Variance defined

The next step is to derive an expression for the scalar variance defined by... 

For a homogeneous scalar field with an isotropic filter, the conditional expected value of the scalar will have the property (+U,

transport equation can be derived for the residual scalar variance defined by11... 

The most popular method of reporting variability is the sample variance, defined as ... 

The population mean and variance defined here may be related to the sample mean and variance, and are given by the following formulas ... 

On the other hand, the sample variance defined by Eq. (1.4) is biased ... 

Both types of variances defined and used in the previous section play a central role in the analysis of variance (ANOVA). This is because of the assumption that s%prod measures the scatter of data caused by systematic factors (in the above section the factor laboratory ) and s2epeat measures the random scatter of data. Hence we will need this principle in the interpretation of the results from experimental design. 

For dispersion variance, defined as the mean value of the square of the difference between the variable n and its mean value n,r = 2. 

The analysis also gives consistent expressions for the Gaussian variances defining the hazard area envelope resulting from a meandering plume, e.g. Figure 7. 

The asymptotic method Here we choose the interarrival-time SCV of the renewal process so that its asymptotic variance [defined in (18)] agrees with that of N. This means we choose so that... 

Suppose that in a set of n values of b, each has a known population variance, erf. The sample variance, (defined by Eq. (18.2)) is actually an unbiased estimate of the population variance, a , which is defined as... 

For a two-component mixture, write down expressions for (a) mean composition, (b) estimated variance when the true mean is unknown, (c) upper and lower theoretical limits of mixture variance. Define all symbols used. 

The accuracy of calibrations for the determination of protein in straight-grade flour when assessed on samples differing from those used in the calibration is of the order of 0.20% expressed as a standard error of prediction (SEP) [1,3,5]. Further, the calibrations have been found to be applicable to a wide range of sample types [1,3] and stable over a long period of time without adjustment [3]. Because NIR is being used as a practical tool to check bakery flour specifications [2], it is inevitable that disputes will arise between the supplier and the baker as to the accuracy of the NIR calibration. The usual course of action in such circumstances would be to analyze the disputed sample by the reference method, when almost certainly a discrepancy will be found between this result and the NIR result. This does not necessarily mean, however, that the calibration requires adjustment. The reason is to be found by partitioning the variance defined by the SEP [5]. 

---