Expected value formula: expected value = ∑ (possible result x its possibility).
Where the ∑ sign indicates summation, and the possible results are possible events, and the possibility indicates the probability of each possible result. For example, suppose a person draws one lottery ticket from a stack of 100 yuan, and he has a 20% chance of winning the triple prize (300 yuan) and an 80% chance of winning the ordinary 100 yuan lottery ticket.
The expected value can be obtained by the formula of expected value: expected value = (300 * 0.2)+(100 * 0.8) = 60+80 =140. Therefore, this person's expectation of drawing tickets is 140 yuan.
In addition, the expected value can also be used to offset the uncertainty, and the statistics of a random variable can be calculated by calculating the expected value. An expected value of 0 means that the investment income equals the risk, an expected value of less than 0 means that the risk is better than the dry income, and an expected value of 0 means that the income is better than the risk, so a reasonable investment choice can be made according to the expected value.
The difference between expected utility and expected utility;
Expected value is an objective mathematical concept, which refers to the average or expected value of a group of possible results. In probability theory and statistics, expected value is usually used to describe the distribution of a random variable, which can be regarded as the center or average of the whole distribution. Expectation value does not involve the subjective wishes and preferences of specific individuals, but a mathematical description of a set of possible results.
Expected utility is a subjective concept, which involves the subjective wishes and preferences of specific individuals. Expected utility refers to the level of utility that an individual expects to obtain under the risk or uncertainty. It is based on personal preference and judgment of different possible outcomes and is calculated through a certain probability distribution.
Simply put, expected value is an objective mathematical concept, while expected utility is a subjective concept. Expected value describes the average or expected value of a group of possible results, while expected utility is the judgment level of individual's preference and expectation for different possible results. These two concepts play an important role in probability theory and mathematical statistics, but their emphasis and significance are different.