已知随机变量x,y的相关系数pxy=1⼀2

2025-04-07 21:57:01
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回答1:

E(X)=1 D(X)=9,E(Y)=0,D(Y)=4 由P=-1/2 p=[E(X)E(Y)-E(XY)]/根下D(X)根下D(Y) 得E(XY)=3 D(Z)=D(1/3 X+1/2 Y)=E(1/3 X+1/2 Y)^2-[E(1/3 X+1/2 Y)]^2 =1/9E(X^2)+1/4E(Y^2)+1/3E(XY)-(1/3E(X)+1/2E(Y))^2 由E(X^2)=D(X)+E(X)^2 D(Z)=87/36