In probability theory, the expected value of a random variable, intuitively, is the long-run average value of repetitions of the experiment it represents
. , which is basically equivalent to the expected number of "expected value".
If X is a random variable in the probability space (Ω, F, P), then its expected value E[X] is defined as:
That is, the sum of each possible outcome in an experiment multiplied by its outcome probability.
The basic properties of expectations are:
- linear
- In general, the expected value of the product of two random variables is not equal to the product of the expected values of the two random variables.
- When E[XY]=E[x]E[y] holds, the covariance of random variables X and Y is 0, that is, they are not correlated. In particular, when two random variables are independent, their covariance (if any) is 0.
- The expected value can also be calculated by the variance calculation formula
