exercise:27d8a676f7: 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>X_1</math>, <math>X_2</math>, \ldots, <math>X_n</math> be an independent trials process, with values in <math>\{0,1\}</math> and mean <math>\mu = 1/3</math>. Find the ordinary and moment generating functions for the distribution of <u...") |
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Let <math>X_1</math>, <math>X_2</math>, ..., <math>X_n</math> be an independent trials | |||
process, with values in <math>\{0,1\}</math> and mean <math>\mu = 1/3</math>. Find the ordinary and | process, with values in <math>\{0,1\}</math> and mean <math>\mu = 1/3</math>. Find the ordinary and | ||
moment generating functions for the distribution of | moment generating functions for the distribution of | ||
<ul><li> <math>S_1 = X_1</math>. '' Hint'': First find <math>X_1</math> explicitly. | <ul style="list-style-type:lower-alpha"><li> <math>S_1 = X_1</math>. '' Hint'': First find <math>X_1</math> explicitly. | ||
</li> | </li> | ||
<li> <math>S_2 = X_1 + X_2</math>. | <li> <math>S_2 = X_1 + X_2</math>. | ||
Latest revision as of 00:45, 15 June 2024
Let [math]X_1[/math], [math]X_2[/math], ..., [math]X_n[/math] be an independent trials process, with values in [math]\{0,1\}[/math] and mean [math]\mu = 1/3[/math]. Find the ordinary and moment generating functions for the distribution of
- [math]S_1 = X_1[/math]. Hint: First find [math]X_1[/math] explicitly.
- [math]S_2 = X_1 + X_2[/math].
- [math]S_n = X_1 + X_2 +\cdots+ X_n[/math].