Search results
Results From The WOW.Com Content Network
In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first moment) is a generalization of the weighted average.
In quantum mechanics, the expectation value is the probabilistic expected value of the result (measurement) of an experiment. It can be thought of as an average of all the possible outcomes of a measurement as weighted by their likelihood, and as such it is not the most probable value of a measurement; indeed the expectation value may have zero probability of occurring (e.g. measurements which ...
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 probability theory and statistics, the law of the unconscious statistician, or LOTUS, is a theorem which expresses the expected value of a function g(X) of a random variable X in terms of g and the probability distribution of X.
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 ...
That the probability distribution describing the next outcome may grow increasingly similar to a certain distribution; Some less obvious, more theoretical patterns could be That the series formed by calculating the expected value of the outcome's distance from a particular value may converge to 0
Expected value of sample information, the expected increase in utility that a decision-maker could obtain from gaining access to a sample of additional observations before making a decision Expected value of including uncertainty , the expected difference in the value of a decision based on a probabilistic analysis versus a decision based on an ...
When two random variables are statistically independent, the expectation of their product is the product of their expectations. This can be proved from the law of total expectation : E ( X Y ) = E ( E ( X Y ∣ Y ) ) {\displaystyle \operatorname {E} (XY)=\operatorname {E} (\operatorname {E} (XY\mid Y))}