2. The continuous random variables X and Y have known joint probability density function f(x,y) given by fw(x, y) = {(x+y)/8 0≤x≤ 2,0 ≤ys 2 0 otherwise. Define the random variable z as Z = min(X,Y). a) Determine the probability density function (²) 7 f₂(z) of the random variable Z. b) Determine the probability

7. Let X and Y denote two continuous random variables. Let f(x,y) denote the joint probability density function and fx(x) and fy (y) the marginal probability density functions for X and Y, respectively. Finally let Z = aX + bY, where a and b are non-zero real numbers. (e) Derive an expression for Cov(Z) as a function of Var (X), Var(Y) and Cov(X,Y). [You may use standard results relating to variance and covariance without proof, but these should be clearly stated.]