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A well defined expectation implies that there is one number, or rather, one constant that defines the expected value. Thus follows that the expectation of this constant is just the original expected value.
A function is well defined if it gives the same result when the representation of the input is changed without changing the value of the input. For instance, if f {\displaystyle f} takes real numbers as input, and if f ( 0.5 ) {\displaystyle f(0.5)} does not equal f ( 1 / 2 ) {\displaystyle f(1/2)} then f {\displaystyle f} is not well defined ...
Interpretation of PAE values allows scientists to understand the level of confidence in the predicted structure of a protein: Lower PAE values between residue pairs from different domains indicate that the model predicts well-defined relative positions and orientations for those domains.
The expected value of random variable X is typically written as E(X) for the expectation operator, and for the parameter. experiment Any procedure which can be infinitely repeated and which has a well-defined set of outcomes. exponential family event
The proposition in probability theory known as the law of total expectation, [1] the law of iterated expectations [2] (LIE), Adam's law, [3] the tower rule, [4] and the smoothing theorem, [5] among other names, states that if is a random variable whose expected value is defined, and is any random variable on the same probability space, then
In this case, the structure of the real numbers makes it possible to define quantities such as the expected value and variance of a random variable, its cumulative distribution function, and the moments of its distribution. However, the definition above is valid for any measurable space of values.
It is well known that any non-decreasing càdlàg function F with limits F(−∞) = 0, F(+∞) = 1 corresponds to a cumulative distribution function of some random variable. There is also interest in finding similar simple criteria for when a given function φ could be the characteristic function of some random variable.
In probability theory, the conditional expectation, conditional expected value, or conditional mean of a random variable is its expected value evaluated with respect to the conditional probability distribution. If the random variable can take on only a finite number of values, the "conditions" are that the variable can only take on a subset of ...