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Expected values can also be used to compute the variance, by means of the computational formula for the variance = [] ( []). A very important application of the expectation value is in the field of quantum mechanics .
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 ...
In probability theory and statistics, variance is the expected value of the squared deviation from the mean of a random variable. The standard deviation (SD) is obtained as the square root of the variance.
The expected return (or expected gain) on a financial investment is the expected value of its return (of the profit on the investment). It is a measure of the center of the distribution of the random variable that is the return. [1] It is calculated by using the following formula: [] = = where
All of the cumulants of the Poisson distribution are equal to the expected value λ. The n th factorial moment of the Poisson distribution is λ n . The expected value of a Poisson process is sometimes decomposed into the product of intensity and exposure (or more generally expressed as the integral of an "intensity function" over time or space ...
For a random variable following the continuous uniform distribution, the expected value is = +, and the variance is = (). For the special case a = − b , {\displaystyle a=-b,} the probability density function of the continuous uniform distribution is:
The expected value and variance of a geometrically distributed ... Substituting this estimate in the formula for the expected value of a geometric distribution and ...
The expected value of g(X) is then identified as (()) ′ = (), where the equality follows by another use of the change-of-variables formula for integration. This shows that the expected value of g ( X ) is encoded entirely by the function g and the density f of X .