exercise:7f4489e357: 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> Let <math>p</math> and <math>p'</math> be the two distributions <math display="block"> p = \pmatrix{ 1 & 2 & 3 & 4 & 5 \cr 1/3 & 0 & 0 & 2/3 & 0 \cr}\ , </math> <math display="block"> p' = \pmatrix{ 1 & 2 & 3 & 4 & 5 \cr 0 & 2/3 & 0 & 0 & 1/3...") |
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Let <math>p</math> and <math>p'</math> be the two distributions | |||
<math display="block"> | <math display="block"> | ||
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0 & 2/3 & 0 & 0 & 1/3 \cr}\ . | 0 & 2/3 & 0 & 0 & 1/3 \cr}\ . | ||
</math> | </math> | ||
<ul><li> Show that <math>p</math> and <math>p'</math> have the same first and second moments, but not | <ul style="list-style-type:lower-alpha"><li> Show that <math>p</math> and <math>p'</math> have the same first and second moments, but not | ||
the same third and fourth moments. | the same third and fourth moments. | ||
</li> | </li> | ||
Latest revision as of 23:44, 14 June 2024
Let [math]p[/math] and [math]p'[/math] be the two distributions
[[math]]
p = \pmatrix{
1 & 2 & 3 & 4 & 5 \cr
1/3 & 0 & 0 & 2/3 & 0 \cr}\ ,
[[/math]]
[[math]]
p' = \pmatrix{
1 & 2 & 3 & 4 & 5 \cr
0 & 2/3 & 0 & 0 & 1/3 \cr}\ .
[[/math]]
- Show that [math]p[/math] and [math]p'[/math] have the same first and second moments, but not the same third and fourth moments.
- Find the ordinary and moment generating functions for [math]p[/math] and [math]p'[/math].