Let [math]X_1[/math], [math]X_2[/math], ..., [math]X_n[/math] be an independent trials process, with values in [math]\{0,1\}[/math] and mean [math]\mu = 1/3[/math]. Find the ordinary and moment generating functions for the distribution of

• [math]S_1 = X_1[/math]. Hint: First find [math]X_1[/math] explicitly.
• [math]S_2 = X_1 + X_2[/math].
• [math]S_n = X_1 + X_2 +\cdots+ X_n[/math].