设随机变量X与Y相互独立，且E(X)＝E(Y)=1，D(X)＝2，D(Y)＝3，试求D(XY)．

【答案】：D(XY)=E(X²Y²)-[E(XY)]²，
由X，Y相互独立知，X²与Y²也相互独立，所以
D(XY)＝E(X²)E(Y²)-[E(X)E(Y)]²
＝{D(X)+[E(X)]²}{D(Y)+[E(Y)]²}
-[E(X)]²[E(Y)]²
＝(2+1)(3+1)-1²×1²＝11．

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