Question

设随机变量X的分布列为X | -1 0 1— |———————P |1/3 1/3 1/3|Y=X^2,试证X与Y不相关

Answer 1

ecause EX=(-1*1/3)+0*1/3+1*1/3 =0;EXY=EX^3=(1/3)*(-1)^3+(1/3)1^3=0;

COV(XY)=EXY-EXEY=0;P(X=1,Y=0)=0,P(Y=0)=P(X=0)=1/3;

P(X=1)*P(X=0)=1/3 * 1/3 =1/9,

then P(X=1,Y=0)=0,but P(X=1)*P(X=0)=1/3 * 1/3 =1/9.the conclusion be hold.