求一道概率论与数理统计的题目答案,没有解题步骤的就不要参与回答了,谢谢!
1个回答
2016-11-03 · 知道合伙人教育行家
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E(X)=0·(q+0)+1·(0+p)=p
E(X²)=0²·(q+0)+1²·(0+p)=p
D(X)=E(X²)-E²(X)=p-p²=pq
E(Y)=0·(q+0)+1·(0+p)=p
E(Y²)=0²·(q+0)+1²·(0+p)=p
D(Y)=E(Y²)-E²(Y)=p-p²=pq
E(XY)=0·0·q+0·1·0+1·0·0+1·1·p=p
Cov(X,Y)=E(XY)-E(X)·E(Y)
=p-p²=pq
∴ρXY=Cov(X,Y)/[√D(X)·√D(Y)]
=pq/(pq)
=1
E(X²)=0²·(q+0)+1²·(0+p)=p
D(X)=E(X²)-E²(X)=p-p²=pq
E(Y)=0·(q+0)+1·(0+p)=p
E(Y²)=0²·(q+0)+1²·(0+p)=p
D(Y)=E(Y²)-E²(Y)=p-p²=pq
E(XY)=0·0·q+0·1·0+1·0·0+1·1·p=p
Cov(X,Y)=E(XY)-E(X)·E(Y)
=p-p²=pq
∴ρXY=Cov(X,Y)/[√D(X)·√D(Y)]
=pq/(pq)
=1
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