is the interval grey linguistic variables, we can get the ranking alternatives by the expectation value
Each run provides two independent z values, one determined by the deviation of the total number of events from its expectation value of 40, the other determined by the deviation of Pot from its expectation value.
For each run, the value of Pot was calculated, and a corresponding z value was derived, using the exact theoretical values for expectation value and variance supplied by Equations 8 and 9.
Actually these values compose an extremely interesting data set to analyze, since the expectation values can be calculated by quantum mechanics from exact analytical wave functions and do not have any measurement error (errors in physical constants such as a0 and h can be neglected).
Therefore, it can be requested that Muller's model must reproduce these expectation values exactly, which is indeed possible, but only when introducing a further modification to the model.
D and F have the theoretical expectation value of 10,000/2 = 5,000, and the theoretical variance of 10,000/4 = 2,500, with |Sigma~ = 50.
With the pointer starting at P = 3 and then randomly moving over the range from 0 to 6, the expectation value of the sum of the 128 values was 3 x 128 = 384.
It characterises two parameters of the random variable distribution, namely, the expectation value
This is reflected in the fact that the expectation value for 0 for a system in state W is:
Thus, the interference terms in the calculation of the expectation value for 0 on the state [Psi] will be zero.
The rule for calculating the expectation values
for observables from the wave function is called Born's Rule, the equation describing evolution outside measurement contexts is Schroedinger's equation, and finally the rule describing state transitions during measurement is the collapse postulate.
For example, you may be in the situation we envisaged above, changing some of the values of your prior probability; alternatively, you may have a great deal of sample evidence which you choose to interpret as determining specific expectation values
for the events concerned (we shall discuss the status of expectation values
as legitimate data in our concluding section).