Question

一道概率论的题！！！在线等！！

设D（X）=3，Y=3X+1，则相关系数pXY=？
本人基础十分差 求详细步骤 谢谢！

Answer 1

E(Y)=E(3X+1)=3E(X)+1； D(Y)=D(3X+1)=9D(X)=27； E(XY)=E(3X^2+X)=3E(X^2)+E(X) =3{D(X)+[E(X)]^2}+E(X) =3D(X)+3[E(X)]^2+E(X) =9+3[E(X)]^2+E(X) C(X，Y)=E(XY)-E(X)E(Y) =9+3[E(X)]^2+E(X)-E(X)[3E(X)+1] =9+3[E(X)]^2+E(X)-3[E(X)]^2-E(X) =9； 所以: ρ(X，Y)=C(X，Y)/{[√D(X)][√D(Y)]} =9/[(√3)(√27)] =1

Answer 2

D（Y）=3*3=9
pXY=