Question

标准差和均值已知X~N（a1,b1),Y~(a2,b2),Z~(a3,b3),X,Y,Z相互独立 M=σx*X+σY*Y

Answer 1

M=√b1X+√b2 Y+√b3 X

E(M)=√b1E(X)+√b2 E(Y)+√b3E(X)=a1√b1+a2√b2+a3√b3

D(M)=D(√b1X+√b2 Y+√b3 X)=b1D(X)+b2 D(Y)+b3D(X)=b1^2+b2^2+b3^2