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Any definition of expected value may be extended to define an expected value of a multidimensional random variable, i.e. a random vector X. It is defined component by component, as E[X] i = E[X i]. Similarly, one may define the expected value of a random matrix X with components X ij by E[X] ij = E[X ij].
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 ...
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
The expected value or mean of a random vector is a fixed vector [] whose elements are the expected values of the respective random variables. [ 3 ] : p.333 E [ X ] = ( E [ X 1 ] , . . .
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 mean or expected value of an exponentially distributed random variable X with rate parameter λ is given by [] =. In light of the examples given below , this makes sense; a person who receives an average of two telephone calls per hour can expect that the time between consecutive calls will be 0.5 hour, or 30 minutes.
where μ is the expected value of the random variables, σ equals their distribution's standard deviation divided by n 1 ⁄ 2, and n is the number of random variables. The standard deviation therefore is simply a scaling variable that adjusts how broad the curve will be, though it also appears in the normalizing constant .
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. The form of the law depends on the type of random variable X in question.