D的面积S=1/2,密度函数f(x,y)=2,(x∈D).
E(X)=∫∫[D]xf(x,y)dxdy
=∫[0,1]2xdx∫[0,1-x]dy
=∫[0,1]2x(1-x)dx
=(x^2-2x^3/3)|[0,1]
=1/3.
E(X^2)=∫∫[D]x^2f(x,y)dxdy
=∫[0,1]2x^2dx∫[0,1-x]dy
=∫[0,1]2x^2(1-x)dx
=(2x^3/3-2x^4/4)|[0,1]
=1/6.
D(X)=E(X^2)-[E(X)]^2=1/6-(1/3)^2=1/18.
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