=E{X^2-2*X*E[X]+E[X]^2}

=E[X^2]-E{2*X*E[X]}+E{E[X]^2}

=E[X^2]-2*E[X]*E[X]+E[X]^2

=X[X^2]-E[X]^2

Variance in probability theory is used to measure the deviation between random variables and their mathematical expectations (that is, the mean value). The variance (sample variance) in statistics is the average value of the square of the difference between each sample value and the average value of all sample values. In many practical problems, it is of great significance to study variance or deviation.

Extended data:

Both discrete random variables and continuous random variables are determined by the range of random variables.

Variables can only take discrete natural numbers, that is, discrete random variables. For example, if you toss 20 coins at a time, K coins face up, and K is a random variable. The value of k can only be a natural number 0, 1, 2, …, 20, but not a decimal 3.5, so k is a discrete random variable.

If a variable can take any real number in a certain interval, that is, the value of the variable can be continuous, then this random variable is called a continuous random variable. For example, the bus runs every 15 minutes, and the waiting time of people on the platform is a random variable. The value range of X is [0, 15], which is an interval. Theoretically, any real number 3.5 can be taken in this interval, so it is called a continuous random variable.

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