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(Created page with "<div class="d-none"><math> \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}</math></div> 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>. <ul><li> Find its ordinary generating function <math>h(z)</math>. </li> <li> Using (a), find its moment gener...") |
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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>. | |||
<ul style="list-style-type:lower-alpha"><li> Find its ordinary generating function <math>h(z)</math>. | |||
moments <math>\mu_1 = 1</math>, <math>\mu_2 = 3/2</math>. | |||
<ul><li> Find its ordinary generating function <math>h(z)</math>. | |||
</li> | </li> | ||
<li> Using (a), find its moment generating function. | <li> Using (a), find its moment generating function. | ||
Latest revision as of 23:43, 14 June 2024
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].