Let [math]X_1[/math], [math]X_2[/math], ..., [math]X_n[/math] be an independent trials process with normal density of mean 1 and variance 2. Find the moment generating function for

• [math]X_1[/math].
• [math]S_2 = X_1 + X_2[/math].
• [math]S_n = X_1 + X_2 +\cdots+ X_n[/math].
• [math]A_n = S_n/n[/math].
• [math]S_n^* = (S_n - n\mu)/\sqrt{n\sigma^2}[/math].