设X与Y为随机变量,E(X)=3 E(Y)=-2 D(X)=9 D(Y)=4.在下列情况下,求E(3X-Y) ,D(3X-Y)(1)COV(X,Y)=1(2)COV(X,Y)=0(3)COV(X,Y)=-1D(3X-Y) = 9D(X)+D(Y) - 2COV(3X,Y) = 9D(X)+D(Y) - 6COV(X,Y)这一步是怎麼弄出来的,望指教,
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![设X与Y为随机变量,E(X)=3 E(Y)=-2 D(X)=9 D(Y)=4.在下列情况下,求E(3X-Y) ,D(3X-Y)(1)COV(X,Y)=1(2)COV(X,Y)=0(3)COV(X,Y)=-1D(3X-Y) = 9D(X)+D(Y) - 2COV(3X,Y) = 9D(X)+D(Y) - 6COV(X,Y)这一步是怎麼弄出来的,望指教,](/uploads/image/z/12664906-34-6.jpg?t=%E8%AE%BEX%E4%B8%8EY%E4%B8%BA%E9%9A%8F%E6%9C%BA%E5%8F%98%E9%87%8F%2CE%28X%29%3D3+E%28Y%29%3D-2+D%28X%29%3D9+D%28Y%29%3D4.%E5%9C%A8%E4%B8%8B%E5%88%97%E6%83%85%E5%86%B5%E4%B8%8B%2C%E6%B1%82E%283X-Y%29+%2CD%283X-Y%29%281%29COV%28X%2CY%29%3D1%282%29COV%28X%2CY%29%3D0%283%29COV%28X%2CY%29%3D-1D%283X-Y%29+%3D+9D%28X%29%2BD%28Y%29+-+2COV%283X%2CY%29+%3D+9D%28X%29%2BD%28Y%29+-+6COV%28X%2CY%29%E8%BF%99%E4%B8%80%E6%AD%A5%E6%98%AF%E6%80%8E%E9%BA%BC%E5%BC%84%E5%87%BA%E6%9D%A5%E7%9A%84%EF%BC%8C%E6%9C%9B%E6%8C%87%E6%95%99%EF%BC%8C)
设X与Y为随机变量,E(X)=3 E(Y)=-2 D(X)=9 D(Y)=4.在下列情况下,求E(3X-Y) ,D(3X-Y)(1)COV(X,Y)=1(2)COV(X,Y)=0(3)COV(X,Y)=-1D(3X-Y) = 9D(X)+D(Y) - 2COV(3X,Y) = 9D(X)+D(Y) - 6COV(X,Y)这一步是怎麼弄出来的,望指教,
设X与Y为随机变量,E(X)=3 E(Y)=-2 D(X)=9 D(Y)=4.在下列情况下,求E(3X-Y) ,D(3X-Y)
(1)COV(X,Y)=1
(2)COV(X,Y)=0
(3)COV(X,Y)=-1
D(3X-Y) = 9D(X)+D(Y) - 2COV(3X,Y) = 9D(X)+D(Y) - 6COV(X,Y)这一步是怎麼弄出来的,望指教,
设X与Y为随机变量,E(X)=3 E(Y)=-2 D(X)=9 D(Y)=4.在下列情况下,求E(3X-Y) ,D(3X-Y)(1)COV(X,Y)=1(2)COV(X,Y)=0(3)COV(X,Y)=-1D(3X-Y) = 9D(X)+D(Y) - 2COV(3X,Y) = 9D(X)+D(Y) - 6COV(X,Y)这一步是怎麼弄出来的,望指教,
E(3X-Y) = 3E(X)-E(Y)
D(3X-Y) = 9D(X)+D(Y) - 2COV(3X,Y) = 9D(X)+D(Y) - 6COV(X,Y)
(1)、E(X) = 3*3-(-2) = 11
D(X) = 9*9+4-6 = 79
(2)、E(X) = 11
D(X) = 9*9+4-0=85
(3)、E(X)= 11
D(X)= 9*9+4-6*(-1)=91
(1)、(2)、(3)中的期望结果一样,方差算法根据协方差的不同而有所不同
回复你:
这个是方差性质公式,要记住的,解题时直接用:
D(aX+bY)=a^2D(X)+b^2D(Y)+2COV(aX,bY)=a^2D(X)+b^2D(Y)+2abCOV(X,Y)
D(aX-bY)=a^2D(X)+b^2D(Y)-2COV(aX,bY)=a^2D(X)+b^2D(Y)-2abCOV(X,Y)
这两个看起来长,其实很简单,单个看:
D(X+Y)=D(X)+D(Y)+2COV(X,Y)
D(X-Y)=D(X)+D(Y)-2COV(X,Y)
这两个是方差的原始性质公式
D(aX)=a^2D(x)
方差性质:把a提出来要加平方
cov(aX,bY)=abcov(X,Y)
协方差性质公式:就是a,b可以直接提出来
把这几个小公式合到一起就是我上面写的那两个长的