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 S{(r² + y°), Osx s1;0sy s1 {6. f(x, y) = elsewhere. (a) If Z=X+ Y, the sum of the two proportions, find E(Z) ; (b) Find E(XY ); (c) Find Var(X); (d) Find Cov(X, Y );