Question

Random variables X and Y assume values 1, 2 and 3.
Their joint probability distribution is given as follows:
P(X=Y=1) = min( 0.32, 0.5 ) ,
P(X=Y=2) = min( 0.18, 0.18 ) and  
P(X=Y=3) = min( 0.5 0.32, ), ....
Their marginal probability distributions are as follows:
P(X=1) = 0.32, P(Y=1) = 0.5,   
P(X=2) = 0.18, P(Y=2) = 0.18,
P(X=3) = 0.5 and P(Y=3) = 0.32,   
Calculate the variance of the sum (X + Y).

Answer 1