The two formulas for variance calculation are S2 =1/n [(x1-m) 2+(x2-m) 2+(xn-m) 2], and s = √ {1/n [(x)].
In probability theory and mathematical statistics, mathematical expectation (or simply mean, or expectation) is the sum of the possible results multiplied by the results in each experiment, which is one of the most basic mathematical characteristics. It reflects the average value of random variables.
Variance In probability theory and statistics, the variance of a random variable describes its deviation, that is, the distance between the variable and its expected value. The variance of a real random variable is also called its second-order moment or second-order central dynamic difference, which happens to be its second-order cumulant. This is to square each error, add it, and then divide it by the total. In this way, the distribution and fragmentation degree of each data can be calculated.
Extended data:
Expectation is like a random experiment repeated many times under the same opportunity, and the average result of all those possible states is basically equal to the expected number of "expectation". The expected value may not be equal to every result. In other words, the expected value is the weighted average of the output values of variables. The expected value is not necessarily included in its distribution range, nor is it necessarily equal to the average value of the range.
Gambling is a common application of expectation. For example, there are 38 numbers on the roulette wheel commonly used in the United States, and the probability of each number being selected is equal. Bets are usually placed on one of the numbers. If the output value of roulette wheel is equal to this number, the gambler can get a bonus equivalent to 35 times the bet (excluding the original bet). If the output value is different from the bet number, the bet fails.
Considering all 38 possible outcomes, the expected goal we set here is "winning money". Therefore, if we discuss the two expected states of winning and losing, and bet a number of 1 USD, the expected return is: "The probability of winning is 1, and you can win 35 yuan", plus "37 cases of losing 1 Yuan". In other words, every bet on 1 dollar will lose $0.0526 on average, which means that the expected value of American roulette bet 1 dollar is $0.0526.