exercise:0b6b45f388: 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</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)...") |
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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> | |||
<math>[\,0,\infty)</math> and density <math>f_X</math>. Find the moment generating functions for <math>X</math> | |||
if | if | ||
<ul><li> <math>f_X(x) = 2e^{-2x}</math>. | <ul style="list-style-type:lower-alpha"><li> <math>f_X(x) = 2e^{-2x}</math>. | ||
</li> | </li> | ||
<li> <math>f_X(x) = e^{-2x} + (1/2)e^{-x}</math>. | <li> <math>f_X(x) = e^{-2x} + (1/2)e^{-x}</math>. | ||
Latest revision as of 00:04, 15 June 2024
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].