Expectation
Description
The expected value of a discrete random variable \(X\), symbolized as \(E(X)\), is often referred to as the long-term average or mean (symbolized as \(\mu\)).
The expectation of a random variable is a number that attempts to capture the center of that random variable's distribution. It can be interpreted as the long-run average of many independent samples from the given distribution.
Formula
It is defined as the probability-weighted sum of all possible values in the random variable's support.
\[ E(X) = \mu = \sum xP(x) \]
Example
The below shows the expectation value of a dice:
