随机变量x,y的方差为16和36,相关系数为0.5,求U=3X+2Y与V=X-3Y,的方差...答:解:已知D(X)=16, D(Y)=36, ρ(X,Y)=0.5,已知U=3X+2Y,则D(U)=D(3X+2Y)=9D(X)+4D(Y)+12COV(X,Y)由:,COV(X,Y)=18 所以D(U)=504 D(V)=D(X-3Y)=D(x)+9D(y)-6COV(x,y)=16+936-618=232 ...
几道概率论的习题,请老师同学帮助!答:EX = 1, EY = 3,Z=3X-2Y的均值 EZ = E(3X - 2Y) = 3EX - 2EY = 3 - 2*3 = -3,DX = 5, DY = 8,且X,Y相对独立,所以,Z=3X-2Y的均值和方差 DZ = D(3X - 2Y) = 9DX + 4DY = 9*5 + 4*8 = 77.2,设X服从b(3,p)分布,Z=-2X+5,求X与Z的相关系数ρxz...
概率论计算题设x与y相互独立,x~N(0,1),Y~N(1,2),Z=X+2Y,求x与z的...答:X~N(0,1) =>E(X)= 0, D(X)=1 Y~N(1,2) =>E(Y) = 1, D(Y) =2 Z=X+2Y E(Z)=E(X+2Y)=E(X) +2E(Y) = 0+2=2 D(Z)=D(X+2Y)=D(X) +4D(Y) = 1+8 =9