In a car service station, there are two service lines. The random variables X and Y are the proportions of time that line 1 and line 2 are in use, respectively. The joint probability density function...

Extracted text: In a car service station, there are two service lines. The random variables X and Y are the proportions of time that line 1 and line 2 are in use, respectively. The joint probability density function for (X, Y) is given by f(x, y) ={6," S{(r² + y°), 0sx s1;0sy s1 elsewhere. a) If Z=X+Y, the sum of two proportions, find Var(Z) b) Find Cov (X,Y)