Adding random variables

#1
Hello, i need some help with an assignment.

we have two random variables x1 and x2. E[x1]=E[X2]=1, VAR[X1]=4 and VAR[X2]=5.

Y=1/3(3X1-6X2)

Find VAR[Y],

I think I have to just do this:
1/3(3*VAR[X1]+6*VAR[X2]) and get: 1/3(3*4+6*5)=14

EDIT: COV[X,Y]=1

Can anyone confirm or explain my mistake if it's wrong, thank you so much!
 
Last edited:

obh

Active Member
#2
Please use the following, and show the full step by step
Var(X + Y ) = Var(X) + Var(Y ) + 2cov(X, Y ).
Var[aX + b] = a^2Var(X).
cov (aX, bY) = ab cov (X, Y)