exercise:531abde51b: Difference between revisions

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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> Find the generating functions, both ordinary <math>h(z)</math> and moment <math>g(t)</math>, for the following discrete probability distributions. <ul><li> The distribution describing a fair coin. </li> <li> The distribution describing a fair die....")
 
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<div class="d-none"><math>
Find the generating functions, both ordinary <math>h(z)</math> and moment <math>g(t)</math>, for the following discrete probability distributions.
\newcommand{\NA}{{\rm NA}}
<ul style="list-style-type:lower-alpha"><li> The distribution describing a fair coin.
\newcommand{\mat}[1]{{\bf#1}}
\newcommand{\exref}[1]{\ref{##1}}
\newcommand{\secstoprocess}{\all}
\newcommand{\NA}{{\rm NA}}
\newcommand{\mathds}{\mathbb}</math></div> Find the generating functions, both ordinary <math>h(z)</math>
and moment <math>g(t)</math>, for the following discrete probability distributions.
<ul><li> The distribution describing a fair coin.
</li>
</li>
<li> The distribution describing a fair die.
<li> The distribution describing a fair die.

Latest revision as of 23:39, 14 June 2024

Find the generating functions, both ordinary [math]h(z)[/math] and moment [math]g(t)[/math], for the following discrete probability distributions.

  • The distribution describing a fair coin.
  • The distribution describing a fair die.
  • The distribution describing a die that always comes up 3.
  • The uniform distribution on the set [math]\{n,n+1,n+2,\ldots,n+k\}[/math].
  • The binomial distribution on [math]\{n,n+1,n+2,\ldots,n+k\}[/math].
  • The geometric distribution on [math]\{0,1,2,\ldots,\}[/math] with [math]p(j) = 2/3^{j + 1}[/math].