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D(X-Y)
证明:随机变量x,y不相关的充要条件是
D(X
+
Y)
=D(X)+D(Y)
答:
1、证明充分:由于
D(X
+
Y)
=D(X)+D(Y)+2Cov(x,
y)
,根据
D(X
+
Y)
=D(X)+D(Y),可推出Cov(x,
y)
=0 ,根据相关系数的定义,可以知道相关系数是0,所以x,y不相关。2、证明必要:反之如果
XY
不相关,则相关系数必然为0,而相关系数=Cov(x,y)/[D(X)D(Y)]^(-2),易知分母不能...
证明:随机变量x,y不相关的充要条件是
D(X
+
Y)
=D(X)+D(Y)
答:
1、证明充分:由于
D(X
+
Y)
=D(X)+D(Y)+2Cov(x,
y)
,根据
D(X
+
Y)
=D(X)+D(Y),可推出Cov(x,
y)
=0,根据相关系数的定义,可以知道相关系数是0,所以x,y不相关。2、证明必要:反之如果
XY
不相关,则相关系数必然为0,而相关系数=Cov(x,y)/[D(X)D(Y)]^(-2),易知分母不能为...
概率论是怎样推导
D(X
+
Y)
的?
答:
D(X
+
Y)
=D(X)+D(Y)+2E{[X-EX][Y-EY]} 其中。E{[X-EX][Y-EY]}=E(XY-XEY-YEX+EXEY)=EXY-EXEY-EYEX+EXEY=EXY-EXEY=0 所以:D(X+Y)=D(X)+D(Y)
D
方差计算公式?
答:
D(XY) =
D(X
)D(
Y)
解题过程如下:D(XY) = E{[
XY
-E(XY)]^2} = E{X²Y²-2XYE(XY)+E²(XY)} = E(X²)E(Y²)-2E²(X)E²(Y)+E²(X)E²(Y)= E(X²)E(Y²)-E²(X)E²(Y)如果 E(X) ...
D(x)
是什么?
答:
D(x)
是方差,
D(X)
=E(x²)-[E(X)]²,这是统计学里的公式假设一组数据X:x1,x2,x3,...,x(n-1),xn。X':(x1)²,(x2)²,(x3)²,…,(x(n-1))²,(xn)² 。E(X²)即为X'的期望(此处即为X'的平均值)E(X)即为X的...
d(x
+
y)
协方差的系数怎么取
答:
D(X-Y)
= D(X)+D(Y)-2*Cov(X,Y);D(X) = Cov(X,X) = E(X^2) - E(X)E(X); =>E(X^2) = D(X)+E(X)E(X);协方差性质:Cov(X,Y) = Cov(Y,X);Cov(aX,bY) = abCov(X,Y);Cov(X1+X2,Y) = Cov(X1,Y)+Cov(X2,Y);二. 相关系数 A. 定义 协方差作为...
概率论与数理统计题 证明:若X与Y相互独立,则
D(X
+
Y)
=D(X)+D(Y)_百度...
答:
设Z = X + Y E(Z)=E(X)+E(
Y)
方差的定义:D(Z) = E{(Z-E(Z))²} D(Z) =
D(X
+Y) = E{(X+Y)² - (E(X)+E(Y))²} = E(X² - E²(X)) + E(Y² - E²(Y))+ + E(2XY) - 2E(X) E(Y) = D(X) + D(Y) ...
x,y相互独立时,方差
d(xy)
答:
D(XY) =
D(X
)D(
Y)
解题过程如下:D(XY) = E{[
XY
-E(XY)]^2} = E{X²Y²-2XYE(XY)+E²(XY)} = E(X²)E(Y²)-2E²(X)E²(Y)+E²(X)E²(Y)= E(X²)E(Y²)-E²(X)E²(Y)如果 E(X) ...
为什么X和Y的方差D(XY)=
D(X
) D(
Y)
答:
D(XY) =
D(X
)D(
Y)
解题过程如下:D(XY) = E{[
XY
-E(XY)]^2} = E{X²Y²-2XYE(XY)+E²(XY)} = E(X²)E(Y²)-2E²(X)E²(Y)+E²(X)E²(Y)= E(X²)E(Y²)-E²(X)E²(Y)如果 E(X) ...
方差公式D(XY)=
D(X
) D(
Y)
答:
D(XY) =
D(X
)D(
Y)
解题过程如下:D(XY) = E{[
XY
-E(XY)]^2} = E{X²Y²-2XYE(XY)+E²(XY)} = E(X²)E(Y²)-2E²(X)E²(Y)+E²(X)E²(Y)= E(X²)E(Y²)-E²(X)E²(Y)如果 E(X) ...
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