Revision as of 02:31, 9 June 2024 by Bot (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> For each of the densities in Exercise Exercise, calculate the first and second moments, <math>\mu_1</math> and <math>\mu_2</math>, directly from their definition and verify that <math>g(0) = 1</math>, <math>g'(0) = \mu_1<...")
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Jun 09'24

Exercise

[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]

For each of the densities in Exercise Exercise, calculate

the first and second moments, [math]\mu_1[/math] and [math]\mu_2[/math], directly from their definition and verify that [math]g(0) = 1[/math], [math]g'(0) = \mu_1[/math], and [math]g''(0) = \mu_2[/math].