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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> In Exercise Exercise, the probability distribution is completely determined by its first two moments. Show that this is always true for any probability distribution on <math>\{0,1,2\}</math>. '' Hint'': Given <math>\mu_...") |
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In [[exercise:9076e13f8f |Exercise]], the probability distribution is completely determined by its first two moments. Show that this is always true for any probability distribution on <math>\{0,1,2\}</math>. '' Hint'': Given <math>\mu_1</math> and <math>\mu_2</math>, | |||
find <math>h(z)</math> as in [[exercise:9076e13f8f |Exercise]] and use <math>h(z)</math> to determine <math>p</math>. | |||
completely determined by its first two moments. Show that this is always true for any | |||
probability distribution on <math>\{0,1,2\}</math>. '' Hint'': Given <math>\mu_1</math> and <math>\mu_2</math>, | |||
find <math>h(z)</math> as in | |||
Latest revision as of 00:43, 15 June 2024
In Exercise, the probability distribution is completely determined by its first two moments. Show that this is always true for any probability distribution on [math]\{0,1,2\}[/math]. Hint: Given [math]\mu_1[/math] and [math]\mu_2[/math], find [math]h(z)[/math] as in Exercise and use [math]h(z)[/math] to determine [math]p[/math].