An engineering statistics class has 40 students; 60% are electrical engineering majors, 10% are industrial engineering majors, and 30% are mechanical engineering majors. A sample of four students is selected randomly without replacement for a project team. Let X and Y denote the number of industrial engineering and mechanical engineering majors, respectively.

Determine the following:

(a) f_XY (x, y) 

(b) f_X (x) 

(c) E(X )

(d) f_Y|3 (y) 

(e) E(Y | X = 3)

(f) V (Y | X = 3)

(g) Are X and Y independent?