According to the definition, the sum of the products of all possible values of a discrete random variable and its corresponding probability p is called mathematical expectation, which is denoted as E. If a random variable only obtains a limited number of values: x, y, z, ..., it is called a discrete random variable.

Definition 2

The conventional safety factor that determines the reliability is selected according to experience, that is, the ratio of the average value of material strength limit (called mathematical expectation in probability theory) to the average value of working stress (mathematical expectation).

Mathematical expectation: As early as17th century, a gambler challenged Pascal, a famous French mathematician, and gave him a topic: A and B gamble with equal chances of winning. The rule of the game is that the winner is the one who wins three games first, and the winner can get a reward of 100 francs. In the third game, A won two games and B won one. At this time, the game is suspended for some reason, so how to distribute 100 francs is fair? With the knowledge of probability theory, it is not difficult to know that the probability of A winning the prize is1/2+(1/2)*( 1/2) = 3/4, or the probability of B winning the prize is (1/2) * (12). The word "expectation" appeared in this story, from which mathematical expectation came.