Suppose that X~N(Ux,VARx) and that Y~N(Uy,VARy).

1). Write down the moment generating function Mx(t) = E(e^tx) and My(t) = E(e^ty) of X and Y respectively.

2). If X and Y are independent random variables, derive the moment generating function of the new random variable W=1.2X + 1.5Y.

3). Identify the distribution of W, its expected value and its variance.