Hey Radiance.

Hint for a) If two random variables are independent, then their domains are independent and the result would be that the limits of the integral would just be constants instead of one with dependencies in the limits. Since the limits are dependent, it means that the probabilities are dependent as well (since they represent probabilities).

More formally P(A = a, B = b) = P(A = a)*P(B = b) for independence and the only way this is possible is if Integral over A and B f(a,b)dadb = Integral A f(a)da * Integral B g(b) db.