Let the random variables x and y have joint pdf as follows: f x( , y c ) , = + x y 0 < < x y < < 1 2 , 0 1 a. find the value of constant c. b. find the marginal densities of x and y. c. are the random variables x and y independent? d. find the conditional pdf ’s ( | ) 1f x y and ( | ). 2f y x e. find e x( ) and e y( ). f. find var x( ) and