X ~ n (0 0,4) Mathematical expectation E (x) = 0 and variance D (x) = 4;

Y ~ n (2 2,3/4) Mathematical expectation E (y) = 2 and variance D (y) = 4/3.

X and y are independent of each other:

E(XY)=E(X)E(Y)=0×2=0，

D(X+Y)= D(X)+D(Y)= 4×4/3 = 16/3，

D(2X-3Y)=2？ D(X)-3？ D(Y)=4×4-9×4/3=4

Extended data:

1. Normal distribution properties:

(1) The general normal distribution is denoted as X~N(μ, σ? ), the standard normal distribution is recorded as x ~ n (0, 1).

⑵ Transform general normal distribution into standard normal distribution: If X~N(μ, σ? )，Y=(X-μ)/σ ~N(0， 1)。

⑶ The mathematical expectation of normal distribution is e (x) = μ and d (x) = σ? .

2. Mathematical expectation and variance attributes:

Let c be a constant and x and y be two random variables, which have the following properties:

(1) mathematical expectation properties:

When x and y are independent of each other, E (c) = c, e (CX) = ce (x), e (x+y) = e (x)+e (y), e (xy) = e (x) e (y).

(2) Variance properties:

D(C)=0，D(CX)=C？ D(X), D (X+C) = D (X), when X and Y are independent of each other, D (X+Y) = D (X)+D (Y).

References:

Baidu Encyclopedia _ Mathematical Expectation

Baidu Encyclopedia _ Normal Distribution

Baidu encyclopedia _ variance