Expectation is equal to the random variable multiplied by the corresponding probability, and the random variable can be negative, so expectation may be negative.

Expectation is not necessarily equal to "expectation" in common sense-expectation is not necessarily equal to every result. The expected value is the average of the output values of variables. The expected value is not necessarily contained in the set of output values of variables.

The law of large numbers stipulates that as the number of repetitions approaches infinity, the arithmetic average of numerical values almost inevitably converges to the expected value.

Extended data

Expected economic decision:

Suppose a supermarket sells a certain commodity, the weekly demand X is in the range of 10 to 30, and the purchase quantity of the commodity is also in the range of 10 to 30, so it is possible to obtain value (only once a week). Everything sold in the supermarket can make a profit, 500 yuan.

Supply exceeds demand, the price is reduced, and the loss per unit of goods is 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.

Baidu Encyclopedia-Expectation