Revision as of 03:31, 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> Let <math>X_1</math>, <math>X_2</math>, \ldots, <math>X_n</math> be an independent trials process with density <math display="block"> f(x) = \frac12 e^{-|x|}, \qquad -\infty < x < +\infty\ . </math> <ul><li> Find the mean and variance of <mat...")
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
density
[[math]]
f(x) = \frac12 e^{-|x|}, \qquad -\infty \lt x \lt +\infty\ .
[[/math]]
- Find the mean and variance of [math]f(x)[/math].
- Find the moment generating function for [math]X_1[/math], [math]S_n[/math], [math]A_n[/math], and [math]S_n^*[/math].
- What can you say about the moment generating function of [math]S_n^*[/math] as [math]n \to \infty[/math]?
- What can you say about the moment generating function of [math]A_n[/math] as [math]n \to \infty[/math]?