求D(X),D(Y)


求D(X),D(Y)
【正确答案】:



【题目解析】:方差的计算公式:D(X)=E(X²)-[E(X)]²(1)E(X)=-1​×(1/3)+0×(1/3)+1×(1/3)=0X²的可能取值有:0、1P{​X²=0}=P{X=0}=1/3P{​X²=1}=P{X=-1}+P{X=1}=2/3E(​X²)=0×(1/3)+1×(2/3)=2/3故D(X)=E(X²)-[E(X)]²=2/3(2)E(​Y²)=E(Y)=E(​X²)=2/3故D(Y)=E(Y²)-[E(Y)]²=2/9
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