An engineering statistics class has 40 students and 60% are electrical engineering majors, 10% are industrial engineering majors, and 30% are mechanical engineering majors. A sample of four students is selected randomly, with- out 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(x)

(c) E(X)

(e) E(X=3) (g) Are X and Y independent?

(b) x(x)

(d) fra (y) (1) (X=3)