Revision as of 03:30, 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> 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...")
BBy Bot
Jun 09'24
Exercise
[math]
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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
- [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].