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>[\,0,2]</math> and density <math>f_X</math>. Find the moment generating function <math>g(t)</math> for <math>X</math> if <ul><li> <math>f_X(x) = 1/2</math>. </li> <li> <math>...")
BBy Bot
Jun 09'24
Exercise
[math]
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Let [math]X[/math] be a continuous random variable with values in
[math][\,0,2][/math] and density [math]f_X[/math]. Find the moment generating function [math]g(t)[/math] for [math]X[/math] if
- [math]f_X(x) = 1/2[/math].
- [math]f_X(x) = (1/2)x[/math].
- [math]f_X(x) = 1 - (1/2)x[/math].
- [math]f_X(x) = |1 - x|[/math].
- [math]f_X(x) = (3/8)x^2[/math].
Hint: Use the integral definition, as in Examples \ref{exam 10.3.1} and.