For the random variable x, its expectation can be expressed as e X. Let's see how its variance is expressed:

DX = E(X-EX)2 = E(X2-2 xex+(EX)2)= EX2-(EX)2

So when ex = 0, dx = ex2.

When the random variable X and the random variable Y are independent of each other, we get the following conclusions:

EXY = EX * EY

DXY = ex2ey 2-(EX)2(EY)2

d(X+Y)= DX+DY+2[E(XY)-EXEY]= DX+DY

Common probability distribution:

Uniform distribution: U(a, b), and its corresponding mathematical expectation and variance are:

Mathematical expectation: E(x)=(a+b)/2.

Variance: D(x)=(b-a)2/ 12.