Significance of Expected ValueExpected value (EV) is a central principle in the theory of probability. It is used for average estimation of some random value. Expected value is similar to a center of gravity assuming that the values of probability are the masses of solid point. Let us assume that the game has n different outcomes, probability of each outcome is p_{i}. The expected value of some variable x that takes values x_{i} can be calculated with the next formula: E(x) = x_{1}p_{1 }+ x_{2}p_{2} + ... + x_{n}p_{n} , In case the probabilities of outcomes are equal ( p_{1}=p_{2}=...=p_{n}=1/n ) the expected value equals to arithmetic mean: E(x) = x_{1}/n+ x_{2}/n + ... + x_{n}/n = (x_{1} + x_{2 } + ... + x_{n}) / n Why is the expected value the most important principle in the probability theory? It helps to predict the estimation of some random variable for a long period of trials. The mean of any random variable in a long term gets close to its expected value. This fact is strictly proved in the course of probability theory.
 
