exercise:0e78fd06fb: 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>[\,0,2]</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>...") |
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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> | |||
<math>[\,0,2]</math> and density <math>f_X</math>. Find the moment generating function <math>g(t)</math> for <math>X</math> | |||
if | if | ||
<ul><li> <math>f_X(x) = 1/2</math>. | <ul style="list-style-type:lower-alpha"><li> <math>f_X(x) = 1/2</math>. | ||
</li> | </li> | ||
<li> <math>f_X(x) = (1/2)x</math>. | <li> <math>f_X(x) = (1/2)x</math>. | ||
| Line 19: | Line 12: | ||
</li> | </li> | ||
</ul> | </ul> | ||
'' Hint'': Use the integral definition, as in | |||
10.3.1 | '' Hint'': Use the integral definition, as in [[guide:31815919f9#exam 10.3.1|example]] and [[guide:31815919f9#exam 10.3.2|example]]. | ||
Latest revision as of 00:10, 15 June 2024
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 example and example.