The problem solving process is as follows:

D(XY) = E{[XY-E(XY)]^2}

= E{X？ y？ -2XYE(XY)+E？ (XY)}

= E(X？ )E(Y？ )-2E？ (X)E？ (Y)+E？ (X)E？ (Y)

= E(X？ )E(Y？ )-E？ (X)E？ (Y)？

What if? E(X) = E(Y) = 0，

So what? D(XY) = E(X？ )E(Y？ )= D(X)D(Y)，？

That is, when X and Y are independent of each other and their mathematical expectations are all zero, the variance d (XY) of the product xy of X and Y is equal to:

D(XY) = D(X)D(Y)

It should be noted that the expected value is not necessarily equal to the common sense "expectation"-"expected value" is not necessarily equal to every result. The expected value is the average of the output values of variables. The expected value is not necessarily contained in the set of output values of variables.

The law of large numbers stipulates that as the number of repetitions approaches infinity, the arithmetic average of numerical values almost inevitably converges to the expected value.

Both discrete random variables and continuous random variables of extended data 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 or an irrational number? 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 time x when someone is waiting for the bus on the platform is a random variable.