D是0＜x＜1，0＜y＜x對應的區域，

則

E(X)=∫∫[D]xp(x,y)dxdy

=∫[0~1]dx∫[0~x]2xdy

=∫[0~1]2x²dx

=2/3

E(Y)=∫∫[D]yp(x,y)dxdy

=∫[0~1]dx∫[0~x]2ydy

=∫[0~1]x²dx

=1/3

E(X²)=∫∫[D]x²p(x,y)dxdy

=∫[0~1]dx∫[0~x]2x²dy

=∫[0~1]2x³dx

=1/2

E(Y²)=∫∫[D]y²p(x,y)dxdy

=∫[0~1]dx∫[0~x]2y²dy

=∫[0~1]2/3·x³dx

=1/6

E(XY)=∫∫[D]xyp(x,y)dxdy

=∫[0~1]dx∫[0~x]2xydy

=∫[0~1]x³dx

=1/4

D(X)=E(X²)-E²(X)=1/18

D(Y)=E(Y²)-E²(Y)=1/18

Cov(XY)=E(XY)-E(X)E(Y)=1/36

∴相關係數為

ρ=Cov(XY)÷√[D(X)·D(Y)]=1/2