作业帮1.设随机变量X-N(1,16),Y-N(1,9),ρxy=0.5,令z=x/2+y/1.设随机变量X-N(1,16),Y-N(1,9),ρxy=0.5,令z=x/2+y/3,求ρyz2.设随机变量x服从参数为λ的泊松分布,且已知E[(x-1)(x-2)]=1,则λ=这两题我算的和答案都不一样,
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![1.设随机变量X-N(1,16),Y-N(1,9),ρxy=0.5,令z=x/2+y/1.设随机变量X-N(1,16),Y-N(1,9),ρxy=0.5,令z=x/2+y/3,求ρyz2.设随机变量x服从参数为λ的泊松分布,且已知E[(x-1)(x-2)]=1,则λ=这两题我算的和答案都不一样,](/uploads/image/z/3504968-8-8.jpg?t=1.%E8%AE%BE%E9%9A%8F%E6%9C%BA%E5%8F%98%E9%87%8FX-N%281%2C16%29%2CY-N%281%2C9%29%2C%CF%81xy%3D0.5%2C%E4%BB%A4z%3Dx%2F2%2By%2F1.%E8%AE%BE%E9%9A%8F%E6%9C%BA%E5%8F%98%E9%87%8FX-N%281%2C16%29%2CY-N%281%2C9%29%2C%CF%81xy%3D0.5%2C%E4%BB%A4z%3Dx%2F2%2By%2F3%2C%E6%B1%82%CF%81yz2.%E8%AE%BE%E9%9A%8F%E6%9C%BA%E5%8F%98%E9%87%8Fx%E6%9C%8D%E4%BB%8E%E5%8F%82%E6%95%B0%E4%B8%BA%CE%BB%E7%9A%84%E6%B3%8A%E6%9D%BE%E5%88%86%E5%B8%83%2C%E4%B8%94%E5%B7%B2%E7%9F%A5E%5B%28x-1%29%28x-2%29%5D%3D1%2C%E5%88%99%CE%BB%3D%E8%BF%99%E4%B8%A4%E9%A2%98%E6%88%91%E7%AE%97%E7%9A%84%E5%92%8C%E7%AD%94%E6%A1%88%E9%83%BD%E4%B8%8D%E4%B8%80%E6%A0%B7%2C)
1.设随机变量X-N(1,16),Y-N(1,9),ρxy=0.5,令z=x/2+y/1.设随机变量X-N(1,16),Y-N(1,9),ρxy=0.5,令z=x/2+y/3,求ρyz2.设随机变量x服从参数为λ的泊松分布,且已知E[(x-1)(x-2)]=1,则λ=这两题我算的和答案都不一样,
1.设随机变量X-N(1,16),Y-N(1,9),ρxy=0.5,令z=x/2+y/
1.设随机变量X-N(1,16),Y-N(1,9),ρxy=0.5,令z=x/2+y/3,求ρyz
2.设随机变量x服从参数为λ的泊松分布,且已知E[(x-1)(x-2)]=1,则λ=
这两题我算的和答案都不一样,
1.设随机变量X-N(1,16),Y-N(1,9),ρxy=0.5,令z=x/2+y/1.设随机变量X-N(1,16),Y-N(1,9),ρxy=0.5,令z=x/2+y/3,求ρyz2.设随机变量x服从参数为λ的泊松分布,且已知E[(x-1)(x-2)]=1,则λ=这两题我算的和答案都不一样,
1. 由ρxy=0.5得：Cov(X,Y)=ρxy*√(DX)*√(DY)=0.5*4*3=6
Cov(Y,Z)=Cov(Y,X/2+Y/3)=1/2*Cov(X,Y)+1/3*D(Y)=1/2*6+1/3*9=6
D(Z)=Cov(X/2+Y/3,X/2+Y/3)=Cov(X/2,X/2)+Cov(X/2,Y/3)+Cov(Y/3,X/2)+Cov(Y/3,Y/3)
=1/4*D(X)+1/6*Cov(X,Y)+1/6*Cov(X,Y)+1/9*D(Y)
=1/4*16+1/3*6+1/9*9=7
ρyz=Cov(Y,Z)/[√(DY)*√(DZ)]=6/[3*√7]=2/√7
2. E[(x-1)(x-2)]=E(X^2)-3E(X)+2=D(X)+E^2(X)-3E(X)+2
=λ+λ^2-3λ+2=λ^2-2λ+2=1
λ^2-2λ+1=0,λ=1