The value of XY * * * is

(- 1)*(- 1)= 1, 1*(- 1)=- 1, 2*(- 1)=-2,

(- 1)*2=-2, 1*2=2, 2*2=4

∴ XY=-2，- 1， 1，2，4。

According to various probability values in the joint distribution law, we can get:

P (xy =-2) = 0.2+0.3 = 0.5 (x = 2, y =- 1 and X=- 1, Y=2).

P(XY=- 1)=0.2(X=- 1，Y= 1)，

p(XY = 1)= 0. 1(X =- 1，Y=- 1)，

P(XY=2)=0. 1(X=2，Y= 1)，

P(XY=4)=0. 1(X=2，Y=2)，

∴? e(XY)=(-2)* 0.5+(- 1)* 0.2+ 1 * 0. 1+2 * 0. 1+4 * 0. 1 =-0.5

∴? Finally, we can get E(XY)=-0.5.

Probability theory and mathematical statistics are teaching materials of probability theory and mathematical statistics for the cultivation of applied undergraduate talents in science and engineering. Chapter *** 10 of the book includes: random events and their probabilities, random variables and their distributions, random vectors and their distributions, functions and numerical simulations of random variables, digital characteristics of random variables, law of large numbers and central limit theorem, samples and sampling distributions, parameter estimation, hypothesis testing and MATLAB command realization of probability statistics.