Question

Consider the random variables X and Y with joint pdf given in Problem 2. Obtain the mean and variances of the following random variables:
a) Z= 2X+3Y
b) W=2X-3Y
I already figured out the mean, variance, and correlation coefficient. How do I even do it for Z and W?

Answer 1

The values of the expected values and variance are as follows:
x=1,2,3
y=1,2,3
E[X]=2
E[Y]=2
E[XY]=3.5
Var(X)=0.7
Var(Y)=0.6
Cov(X,Y)=-0.5
p=0.7715

Answer 2

If you would like to see the table as well I will post it as well