Tutorial 5: Joint distribution Function 1. If the joint probability distribution of X and Y is given by f (x, y ) = (x+y) 30 ' -, for x = 0,1,2,3; and y = 0,1,2, find a. P(X 2, Y =1) b. P ( X > 2, Y SI) c. P( X > Y) d. P(X + Y =4) e. marginal distribution of X and Y 2. Let X denote the number of times a certain numerical control machine will malfunction: 1,2, or 3 times on any given day. Let Y denote the number of times a technician is called on an emergency call. Their joint distribution is given as f(x.y) X 2 3 0.05 0.05 0.1 0.05 0.1 0.35 0 0.2 0.1 a. Evaluate the marginal distribution of X b. Evaluate the marginal distribution of Y c. f(X Y = 2) d. Var( X Y =2) 3. If the joint probability density of X and Y is given by f (x, y ) = x+ y, 0 , Z