The summation or integration over all values of a variate of the product of the variate and its probability or its probability density. The expectation is defined by µX-EX xfx dx D. If the random variable X is the top face of a tossed fair six sided die then the probability mass function of X is.
The expected value or mathematical expectation EX of a random variable X is the long-run average value of X that would emerge after a very large number of observations.
To learn a formal definition of EuX the expected value of a function of a discrete random variable. Expectation is the mean earnings in this case if you dont like its utility you are free to use the modal or median values. E X S x 1 p 1 x 2 p 2 x n p n where x is a random variable with the probability function f x p is the probability of the occurrence. To learn a formal definition of EuX the expected value of a function of a discrete random variable.