Expectation, variance and covariance

expect （expectation）： function f(x) On a distribution P(x), When x from P When it comes into being ,f Act on x when ,f(x) Average value . It is the probability of each possible result in the experiment multiplied by the sum of its results .

For discrete random variables , By summing, we get ：

For continuous random variables , By integrating ：

Standard deviation （standard deviation）： When the variance is very small ,f(x) The cluster formed by the value of is close to their expected value . The square of the variance is called the standard deviation .

covariance （covariance）： Measure the overall error of two variables . namely ：

If the absolute value of covariance is large , It means that the variable value changes greatly , And they are also far from their respective averages . If the covariance is positive , So both variables tend to get relatively large values at the same time . If the covariance is negative , So one of the variables tends to get a relatively large value at the same time , Another variable tends to have a relatively small value , vice versa .