Expectation:

EX=3，EY = 1；

dx=e(x^2)-(ex)^2=∫[0→6]( 1/6)x^2dx-9= 12-9=3；

DY = 3；

EZ = E(3X-2Y)= 3EX-2EY = 7；

DZ = D(3X-2Y)= D(3X)+D(-2Y)= 9DX+4DY = 39 .

Extended data

For continuous random variable X, if its definition domain is (a, b) and the probability density function is f(x), the formula for calculating the variance of continuous random variable X is:

D(X)=(x-μ)^2 f(x) dx？ [2]?

Variance describes the dispersion degree between the value of random variable and its mathematical expectation. (The greater the standard deviation and variance, the greater the dispersion)

If the values of x are concentrated, the variance D(X) is small, and if the values of x are scattered, the variance D(X) is large.

Therefore, D(X) is a quantity to describe the dispersion degree of X and a scale to measure the dispersion degree of X..