Expected value

Link: Probability

What is Expected Value? §

Expected value describes the long-term average level of a random variable based on its probability distribution.

Expected value for discrete variables §

Notation for Expected value for discrete variables:

$$E(X)=\sum x\cdot P(X=x)$$

It equals to the sum of each probability of an outcome times the outcome.

Expected value for continuous events §

We calculate the area under the curve of probability, e.g. exponential distribution.

$$E[X]={\int }_{-\infty }^{\infty }x\cdot f(x)\cdot dx$$