Let X take the value 0, 1, or 2 depending on whether there are no customers, between one and 10 customers, and more than 10 customers in the regular (manned)

checkout lines of a supermarket. Let Y be the corresponding variable for the self checkout lines. Find Var(X + Y), when the joint PMF of X and Y is given by

y p(x,y) 0 1 2 Px(x) 0 0.17 0.02 0.01 0.20 x 1 0.150 0.225 0.125 0.50 2 0.060 0.105 0.135 0.30 PY(y) 0.38 0.35 0.27