Suppose that the moment generating function of ((x,Y)prime) is (ψ(x,Y)(t,u)=exp(2t+3u+t²+atu+2u²)). Determine (a) so that (x+2Y) and (2x-Y) become independent.

a) (a = 2)
b) (a = 1)
c) (a = 3)
d) (a = 4)