1, expected to be a definite number, obtained according to the probability distribution. Whether the experiment is carried out or not, we can get the expectation.
Mathematical expectation, also known as mean value, means "the mean value of random variables", and this mean value refers to the weighted average value with probability as the weight.
2, the average (mean), is the average of the sum after doing many experiments.
Extended data:
Application of Mathematical Expectation
1, economic decision-making
Suppose that the weekly demand of a commodity sold in a supermarket is in the range of 10 to 30, and the purchase quantity of the commodity is in the range of 10 to 30 (only once a week). Everything sold in the supermarket can make a profit, 500 yuan. If the supply exceeds the demand, the price will be reduced, and the loss per unit of goods will be 100 yuan.
If the demand exceeds the supply, it can be transferred from other supermarkets. At this time, the goods in the supermarket can make a profit in 300 yuan. When trying to calculate the purchase quantity, the supermarket can get the best profit. And seek the expectation of maximum profit.
Analysis: Because the demand (sales volume) X of this commodity is a random variable, which is evenly distributed in the interval, and the profit value Y of selling this commodity is also a random variable, which is a function of X and is called a function of random variables. The best profit involved in the problem can only be the mathematical expectation of profit (that is, the maximum of average profit).
Therefore, the process of solving this problem is to determine the functional relationship between Y and X, then find the expected E(Y) of Y, and finally find the maximum point and maximum value of E(Y) by extreme value method.
2. Sports competition issues
Table tennis is our national game. In the last century, ice hockey also brought some diplomacy to China. China has an absolute advantage in this sport. Now I want to ask a question about the arrangement of table tennis: Suppose the German national team (German star Bohr also has many fans in China) plays against China.
There are two competition systems, one is three players per team, and the other is five players per team. Which is more beneficial to China?
Analysis: Because of the advantages of China team in this competition, let's assume that the winning percentage of each German player in China team is 60%, and then we only need to compare the corresponding mathematical expectations of the two teams.
Baidu Encyclopedia-Mathematical Expectation