证明若X与Y相互独立则D(XY)=D(X)D(Y)+[E(X)]눀D(Y)+[E(Y)]눀D(X)

2025-03-06 21:38:10
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回答1:

预备知识:①X~N(μ,σ²),则E(X)=μ,D(X)=σ²;②X~U(a,b),则E(X)=(a+b)/2,D(X)=(b-a)²/12;③随机变量X、Y相互独立,则D(X+Y)=D(X)+D(Y)所以,本题中,E(X)=1,D(X)=9,D(Y)=4/3,D(X+3Y)=D(X)+D(3Y)=D(X)+9D(Y)=9+12=21