Let X1,X2,X3 be independent random values with uniform distribution at [0,1]. Calculate E[(X1-2*X2+X3)^2].
I show you what I've done, could you tell me if it's right???
-> E[(X1-2*X2+X3)^2]=E((X1)^2-4*X1*X2+2*X1*X3+4*(X2)^2-4*X2*X3+(X3)^2)=E((X1)^2)+4*E((X2)^2)+E((X3)^2)-4*E(X1)*E(X2)+2*E(X1)*E(X3)-4*E(X2)*E(X3), where E(Xi)=(0+1)/2 and E((Xi)^2)=integral((xi)^2)dxi
Thanks in advance!!!
I show you what I've done, could you tell me if it's right???
-> E[(X1-2*X2+X3)^2]=E((X1)^2-4*X1*X2+2*X1*X3+4*(X2)^2-4*X2*X3+(X3)^2)=E((X1)^2)+4*E((X2)^2)+E((X3)^2)-4*E(X1)*E(X2)+2*E(X1)*E(X3)-4*E(X2)*E(X3), where E(Xi)=(0+1)/2 and E((Xi)^2)=integral((xi)^2)dxi
Thanks in advance!!!