Variance computation

An empirical test of this possibility was performed by computing values of the variance of the two terms in equation 44-77. The Normal random number generator of MATLAB was used to create multiple values of Normally distributed random numbers for Er and Es these were plugged into the two expressions of equation 44-77 and the variance computed. Values between 100 and 106 were used in each computation of the variance. 

Optimum transmittance using 5,000 values in variance computation... 

The reason is that Er determines the distribution that must be used for AEr, and t and AEx together determine Es and hence the distribution of AEs that must be used in the variance computation. 

Excel now goes to work and prints results in cells El to G13 of Figure 4-8. Mean values are in cells F3 and G3. Cells F4 and G4 give variance, which is the square of the standard deviation. Cell F6 gives pooled variance computed with Equation 4-9. That equation was painful to use by hand. Cell F8 shows degrees of freedom (df= 13) and tca cu illed = 20.2 from Equation 4-8 appears in cell F9. 

Variance origin Sumsofthe Degrees Variances Computed value Theoretical differences of freedom of the Fischer value of the... 

Origin of Differences Number of Variances Computed Theoretical value Deci-... 

Origin of the variance Sums of the squares Degrees of freedom Variances Computed value of the Fischer variable Theoretical value of the Fischer variable Decision... 

The analysis of variances using a CFE 2 plan in which, for each experimental point, we produce only one measurement, frequently presents an important residual variance. This result is a consequence of the fact that each point is the result of a particular combination of interaction effects. If, for each experimental point of the plan, we produce more experiments, then we have the normal possibility to compute a real residual variance (5.169). In this situation, the sum is successfully used as shown in Table 5.52 for the residual variance computation. 

Fia. 30. Logarithmic plot of sample variance , computed according to Eq. (57), vs. Dt/L1 (L2). P = proportion of black particles in the overall mixture, D = diffusion coefficient, t = time, L = length of mixer. 

In this formula, X = /n ZhX, is the average value, =- /k-1X(-T, — X) is the standard deviation. The greater of the coefficient of variation, the index s identifieation ability is stronger. According to actual needs, if the coefficient of variation is relatively smaller, the evaluation index could be deleted. According to the above principles, using method of SPSS 16.0 to variance analysis, the evaluation index on the basis of analysis of variance computation in the evaluation system of 31 evaluation index variation analysis, the coefficient of variation of six evaluation indexes is relatively smaller, then they were deleted, and the other 25 indicators were retained, which constitutes the fourth round of safety, quality, progress, investment risk index system. 

Using the formula (11.2.S1) and the independence of measurement errors at r and at times up to t. i, the terms due to r. i-dt., thus to Gk., (11.2.53) will occur additively in the covariance matrix of at t. An assiduous reader can compute them explicitly. Clearly, also the variances computed for the estimated (integrals of the) mass flowrates will remain bounded and wrill not increase dramatically. 

EXAMPLE 1.20 Coin flips mean and variance. Compute the average number of heads in JV = 4 coin flips by using the distribution in Example 1.18 (page 16) ... 

The proposed response spectrum modification procedure ensures correctness of the deterministic seismic analysis of building structures using the response spectrum method. The modification reduces effectively the uncertainties in response due to uncertainties in frequencies causes by variances computation model parameters. 

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