设随机变量X服从正态分布N(0,1).Y=2(X的平方)+X+3,则X 与Y的相关系数是?
设随机变量X服从正态分布N(0,1).Y=2(X的平方)+X+3,则X 与Y的相关系数是?
数学人气:122 ℃时间:2020-02-06 12:14:23
优质解答
E(X)=0,D(X)=E(X^2)=1,E(X^3)= 0 E(X^4)= 3E(Y)=2*E(X^2)+E(X)+3=5E(XY)=2* E(X^3)+ E(X^2)+3* E(X)= 1E(Y^2)=4*E(X^4)+4*E(X^3)+13* E(X^2)+6* E(X)+9=34D(Y)=9COV(X,Y)=E(XY)-E(X)E(Y)=1则X 与Y的相关系数是r=1/3...
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