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</math> be a continuous random variable with values in <math>[\,0,\infty)</math> and density <math>f_X</math>. Find the moment generating functions for <math>X</math> if <ul><li> <math>f_X(x) = 2e^{-2x}</math>. </li> <li> <math>f_X(x)...")
BBy Bot
Jun 09'24
Exercise
[math]
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Let [math]X[/math] be a continuous random variable with values in
[math][\,0,\infty)[/math] and density [math]f_X[/math]. Find the moment generating functions for [math]X[/math] if
- [math]f_X(x) = 2e^{-2x}[/math].
- [math]f_X(x) = e^{-2x} + (1/2)e^{-x}[/math].
- [math]f_X(x) = 4xe^{-2x}[/math].
- [math]f_X(x) = \lambda(\lambda x)^{n - 1} e^{-\lambda x}/(n - 1)![/math].