数学题求解设两个随机变量X,Y的方差分布为25及36,相关系数为0.4,求D(X+Y)及D(X-Y)要有过程谢谢了

Question

数学题求解
设两个随机变量X,Y的方差分布为25及36,相关系数为0.4,求D(X+Y)及D(X-Y)
要有过程
谢谢了

Answer 1

D(X+Y) = DX + DY + 0.4(DX*DY)^(1/2)
= 25 + 36 + 0.4(25*36)^(1/2)
= 25 + 36 + 0.4*5*6
= 25 + 36 + 12
= 73
D(X-Y) = DX + DY - 0.4(DX*DY)^(1/2)
= 25 + 36 - 0.4(25*36)^(1/2)
= 25 + 36 - 0.4*5*6
= 25 + 36 - 12
= 49