Expected average value

Table IV. Analcime. Interatomic Distances in Symmetrized DLS Model and Expected Average Values Corresponding to Si/Al = 2...

Studies of the respiratory quotient or respiratory exchange ratio (RER) indicate a metabolic shift in CR rats depending on food availability, while there is little change in AL rats [21,42]. Figure 7 illustrates daily variations of RER with dietary regimen. Analysis of the food composition indicates an expected average value of RER of 0.89. RER in AL rats is 0.89 0.02 over a 24-hour period and is relatively more constant than that in CR rats, indicating that AL rats metabolize a constant ratio of carbohydrate and lipid over 24 hours [21, 42]. In contrast, CR animals metabolize more carbohydrate... 

You are equally likely to end up with more heads or more tails. Thus, if you tried this a large number of times, the expected average value of M (written M) would be... 

Fig. 4.2.1 The probability density associated with the Gaussian wave packet. The most probable position is at x = xt, which also coincides with the expectation (average) value of the time-dependent position. The width is related to the time-dependent uncertainty (Ax)t, i.e., the standard deviation of the position.

Example 2.3 Using the data in Table 2.1 and from Equation 2.1, we note that the regression equation is y = 6.13 - 0.041x. Suppose the researcher would like to know the expected (average) value of as predicted by x when x, = 15 sec. What is the 95% confidence interval for the expected y average value ... 

Expectation Value Also referred to as expectation, expected value, or mathematical expectation. In simple terms the expectation value for a function of a random variable is the expected average value of the function over a large number of samples. The precise mathematical definition is for a continuous random variable, X,... 

The structures of a series of rhodium complexes, [Rh(L)(CO)2H], of various bisphosphine and bisphosphite ligands, which are equipped with an integral anion binding site, have been studied by Dydio et al Small values of ca. 10 Hz or less found for the phosphorus-hydride coupling at rt have indicated that all bidentate ligands in the complexes under study are coordinated predominantly in the ee fashion (the expected averaged values of /hp fof the ee and ea are around 2 and 100 Hz, respectively). 

It is seen that the three values for the equilibrium constant (k) range from 0.00443 to 0.00565 with an average value of 0.00504. The two values for the densities of the methanol/water associate are in reasonable agreement and have a magnitude that would be expected for the hydrogen bonded associate. 

Using the average value for the equilibrium constant, the distribution concentration of the different components of a methanol water mixture were calculated for initial methanol concentrations ranging from zero to 100%v/v. The curves they obtained are shown in Figure 28. The molar refractivities of 11.88 is also in accordance with that expected since the molar refractivity s of water and methanol are 3.72 and 8.28 respectively. The refractive index of the associate of 1.3502 is, as would be expected, higher than that of either water or methanol. 

Tlie expected value of a random variable is the average value of the random variable. The expected value of a random variable X is denoted by E(X). The expected value of a random variable can be interpreted as the long-run average of observations on tlie random variable. The procedure for calculating the expected value of a random variable depends on whether the random variable is discrete or continuous. 

The process is repeated vvitli another random number until tlie desired 15 simulated values of T have been obtained. The results are shown in Table 20.6.1. Tlie average value of the 15 simulated values of T is 1.02 years, a Monte Carlo estimate of the average life of the pmnp. The true average life of the pump is E(t), tlie expected value of T, obtained by application of Eq. (19.9.2) ... 

A more accurate estimate of the true value of the average life of the pump can be obtained by increasing tlie nmiiber of simulated values in which tlie estimate is based. In tliis example tlie expected value of T, obtained by integration, provided a comparison witli tlie estimated average value of T, obtained by Monte Carlo simulation. Generally Monte Carlo simulation is used to estimate some function of one or more random variables when direct calculation of tliis function would be difficult if not impossible. 

Although 150,000 is somewhat of an average value for expected maximum Kw and uncertainties in the computations make the minimum Kw about 15,000 (below 15,000 no mass transfer to gross surface could be expected to be limiting whereas the maximum possible Kw might be over 1,000,000), assumption 2 certainly gives the more reasonable explanation of the data. 

Expected S value calculated from the regression line from Van Klinken e(ol. (1994) for wood y = (-30.202) h (0.2l4x), where y = expected 6"C and x = the modern July average temperature for the weather station nearest to the site where the sample was coUected-... 

Now run this experiment three times and note the numbers of A and B remaining after each run. Let [A] equal the number of A remaining at the end of the run and [B] the number of B. From your three runs, determine average values and standard deviations for these numbers. We can define the equilibrium constant for the interconversion of A and B as Wgq = [B]/[A]. Determine an average value and standard deviation for this ratio based on your results. What value would you expect for Wgq based on the transition probabilities Does your calculated value from the simulations agree with this value ... 

Plot the numbers of A and B cells versus iterations Determine the average values of [A] and [B] and their standard deviations using the last 500 iterations of the run Determine from these average values Compare the with the expected deterministic value. 

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