Sentence examples for expected value exists from inspiring English sources

Let us agree that a simple (real-valued) random variable on a test space A is a mapping f : E → R where E is a test in A. We define the expected value of f in a state ω ∈ ω(A) in the obvious way, namely, as the expected value of f with respect to the probability weight obtained by restricting ω to E (provided, of course, that this expected value exists).

If its expected value exists, then E[xi]= int_{0}^{1}Phi^{-1}(alpha),mathrm{d}alpha.

If the expected value e exists, then the RUBV can be calculated by overline{V}[xi]= int_{0}^{1}bigl(Phi^{-1} alpha -e bigr)^{2},mathrm{d}alPhi^{-1} alpha -e

This expected value only exists in case N R>L [38].

The addition of these constraints means that even if information allowing positive expected value decisions exists, the potential for the worst case arising from these decisions to breach legal limits eliminates the value to act on this information.

If the expected value e exists, then the variance of ξ satisfies V[xi] leq int_{0}^{+infty} bigl 1-Phi(e+sqrt {x})+Phi (e-sqrt {x}) bigl 1-Phirm{d}x.

The Cauchy distribution, named after Augustin Cauchy, is a simple family of distributions for which the expected value does not exist.

On the other hand, when bias exists, the expected value will not be equal to the true distance.

Since, the obtained values are always ≤ the expected values, there may exist a difference in performance of the linearized/convexified and MINLP solutions.

As the noise is present in microarray datasets, the deviation from actual value and expected value of each element in the dataset also exists.

These values are close to the expected value of Mth10b dimer (19.7 kD), indicating that Mth10b exists primarily as a stable dimer in solution.