设（X、Y)的概率密度为 f(x、y)=｛1/3（x＋y）,0≤x≤1,0≤y≤2, ｛0,其他求D(2x-3y+8)
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亲爱的---分别
∫ f(x,y) dy
∫ f(x,y) dx
fx(x)=(1/3) ∫(0~1) (x+y) dy
=(1/3){xy+y^2/2 (y:0~1)}
=(1/3)(x+1/2)
(0<=x<=2)
=0 else
fy(y)=(1/3){x^2/2+yx (x:0~2)}
=(1/3)(2+2y)
=(2/3)(y+1)
(0<=y<=1)
=0 else
咨询记录 · 回答于2021-11-24
设（X、Y)的概率密度为 f(x、y)=｛1/3（x＋y）,0≤x≤1,0≤y≤2, ｛0,其他 求D(2x-3y+8)
亲爱的---分别∫ f(x,y) dy∫ f(x,y) dxfx(x)=(1/3) ∫(0~1) (x+y) dy=(1/3){xy+y^2/2 (y:0~1)}=(1/3)(x+1/2)(0<=x<=2)=0 elsefy(y)=(1/3){x^2/2+yx (x:0~2)}=(1/3)(2+2y)=(2/3)(y+1)(0<=y<=1)=0 else
不对
亲爱的---你好，
∫ f(x,y) dy
∫ f(x,y) dx
fx(x)=(1/3) ∫(0~1) (x+y) dy
=(1/3){xy+y^2/2 (y:0~1)}
=(1/3)(x+1/2)
(0<=x<=2)
=0 else
fy(y)=(1/3){x^2/2+yx (x:0~2)}
=(1/3)(2+2y)
=(2/3)(y+1)
(0<=y<=1)
=0 else
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