Expected value calculation:
example
A city has 65438+ 10,000 families, 65438+ 10,000 families without children, 90,000 families with one child, 6,000 families with two children and 3,000 families with three children.
Then the number of children in any family in this city is a random variable, recorded as X, which can be taken as 0, 1, 2, 3.
Among them, the probability of x taking 0 is 0.0 1, the probability of 1 is 0.9, the probability of 2 is 0.06, and the probability of 3 is 0.03.
Then, its mathematical expectations
Extended data:
Academic explanation of expectation;
1. Expectation refers to people's subjective estimation of achieved goals;
2. Expectation refers to people's subjective estimation of whether their actions and efforts can lead to expected results, that is, judging the possibility of achieving goals according to individual experience;
3. Expectation refers to the prediction of some incentive efficiency;
4. Expectation refers to the subjective desire of the public for all the connotations such as moral standards, outlook on life and values that individuals or classes in a certain social position and role should have.
Source of expectation:
/kloc-in the 0 th and 7 th centuries, a gambler challenged Pascal, a famous French mathematician, and gave him a topic: A and B gamble, and the chances of winning are equal. The rules of the game are that the winner is the one who wins three games first, and the winner who wins five games can get a reward of 100 francs. In the fourth game, A won two games and B won one. At this time, the game is suspended for some reason, and the distribution of 100 francs is as follows:
With the knowledge of probability theory, it is not difficult to know that A is likely to win and B is unlikely to win. Because the probability of A losing the last two games is only (1/2) × (1/2) =1/4, that is to say, the probability of A winning the last two games is 1-( 1/4) = 3/4, and A has 74. However, if B expects to win 100 francs, it must beat A in the last two games. The probability of B winning the last two games in a row is (1/2) * (1/2) =1/4, that is, B has a 25% probability of winning 100 francs.
It can be seen that although the game can't be played again, according to the above possibilities, the objective expectations of both parties for the final victory are 75% and 25% respectively, so Party A should get 100 * 75% = 75 (francs) and Party B should get 100×25% = 25 (francs). The word "expectation" appeared in this story, from which mathematical expectation came.
Baidu Encyclopedia-Mathematical Expectation