Please provide the answers for the required questions. Solution is a must.

1. Let X and Y be random variables with joint pdf given by fx.x (x, y) = (e-(+>) x>0,y>0 otherwise Find the following: a. Fx.y (x, y) b. fx (x) c. fy (y) 2. Let the three-dimensional random variable (X, Y, Z) have the joint pdf fxxz(x,y,z) = 8xyzl(o.1) (x)/(o.1) (v)/(o.1) Find the following: a. E[3X + 2Y + 62] b. E[XYZ] 3. Consider a sample of size 2 drawn without replacement from an urn containing three balls, numbered 1, 2, and 3. Let X be the number of the first ball drawn, and Y be the larger of the two numbers drawn. a. Find the joint pmf of X and Y b. Find P[X = 1/Y = 3] 4. Let fx.x (x,y) = e-(x*>)1(0.20) (x)/(0.20)(v) a. Find the marginal distributions of X and Y. b. Are X and Y independent