191问答库 > 证明:若随机变量x与y相互独立,则方差满足不等式d(xy)≥d(x)d(y)

证明:若随机变量x与y相互独立,则方差满足不等式d(xy)≥d(x)d(y)

2025-02-23 01:56:01

推荐回答（2个）

回答1：

D(xy)=E(x²y²)-E²(xy)=E(x²)E(y²)-E²(x)E²(y)
D(x)=E(x²)-E²(x)
D(y)=E(y²)-E²(y)
E²(x)>=0
E(x²)>=0
所以
D(x)D(y)=E(x²)E(y²)-E²(x)E²(y)-E²(x)E(y²)-E(x²)E²(y)
=D(xy)-E²(x)E(y²)-E(x²)E²(y)<=D(xy)
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回答2：

离散数学啊忘记离散好多年了