X = {1,2,3,4,5,6}, Y = {1,2,3,4}, Z = {2,4,6,8}. The question is: work out standard deviation of A = 2S-1, where S = the sum of the three random variables.

I know that E(X) = 3.5, E(Y) = 2.5, E(Z) = 5

Var(X) = 2.916, Var(Y) 1.25, Var(Z) = 5

Now in order to find out the standard deviation of A,

am I required to do 2 x the square root of Var(X+Y+Z) -2 ?? (since A = 2S-2), If so then to work out the Var(X+Y+Z) do I need to do Var(X) + Var(Y) + Var(Z) + 2(Cov(X,Y) + Cov(Y,Z) + Cov(X,Z) ??

However Cov(X,Y) and Cov(X,Z) are not defined since there is a different number of elements in the sets. Do I just exclude them from the equation and just do Var(X) + Var(Y) + Var(Z) +2(Cov(Y,Z)

Please help!