Let [math]p[/math] be a probability distribution on [math]\{0,1,2\}[/math] with moments [math]\mu_1 = 1[/math], [math]\mu_2 = 3/2[/math].

• Find its ordinary generating function [math]h(z)[/math].
• Using (a), find its moment generating function.
• Using (b), find its first six moments.
• Using (a), find [math]p_0[/math], [math]p_1[/math], and [math]p_2[/math].