And usually, sigma stands for standard deviation.
1) Calculate E(X + Y) = muX + muY
No, the formula is V(X+Y)=V(X)+V(Y)+2Cov(X,Y)2) Calculate V(X + Y) = sigmaX + sigmaY + 2sigmaXY
where Cov denotes the covariance. Note that Cov(X,Y)=0 if X and Y are independent.
Cov(X,Y)=E[(X-mu(X))(Y-mu(Y))=E(XY)-E(X)E(Y) (the red one is the most commonly used)
3) Calculate E(2X) = 2muX
Exactly the same as above in 3)4) Calculate E(2Y) = ???
For any random variable X (or Y, or whater your variable is called), E(aX)=aE(X)
There is still a problem with the 12sigma(XY), otherwise, it's correct.5) Calculate V(2X + 3Y) = 4sigmaX + 9sigmaY + 12sigmaXY
6) Calculate E(1 + 2X) = 2muX + 1
7) Calculate V(1 + 2X) = 4sigmaX
8) Calculate E(3X + 4(Y + 1)) = 3muX + 4muY + 4
Once again, look at the covariance. Don't hesitate to ask if you don't know what to do.9) Calculate V(3X + 4(Y + 1)) = 9sigmaX + 16sigmaY
10) Calculate E(aX + b(Y + c)) = amuX + bmuY + bc
Once again, the formula for the variance is false11) Calculate V(aX + b(Y + c)) = a^2sigmaX + b^2sigmaY
Good working anyway, it's good to see someone's attempts :P