exercise:C5cdb3a223: 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>[\,0,1]</math>, uniform density function <math>f_X(x) \equiv 1</math> and moment generating function <math>g(t) = (e^t - 1)/t</math>. Find in terms of <math>g(t)</math> the...") |
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Let <math>X</math> be a continuous random variable with values in <math>[\,0,1]</math>, | |||
uniform density function <math>f_X(x) \equiv 1</math> and moment generating function <math>g(t) = (e^t | uniform density function <math>f_X(x) \equiv 1</math> and moment generating function <math>g(t) = (e^t | ||
- 1)/t</math>. Find in terms of <math>g(t)</math> the moment generating function for | - 1)/t</math>. Find in terms of <math>g(t)</math> the moment generating function for | ||
<ul><li> <math>-X</math>. | <ul style="list-style-type:lower-alpha"><li> <math>-X</math>. | ||
</li> | </li> | ||
<li> <math>1 + X</math>. | <li> <math>1 + X</math>. | ||
Latest revision as of 00:05, 15 June 2024
Let [math]X[/math] be a continuous random variable with values in [math][\,0,1][/math], uniform density function [math]f_X(x) \equiv 1[/math] and moment generating function [math]g(t) = (e^t - 1)/t[/math]. Find in terms of [math]g(t)[/math] the moment generating function for
- [math]-X[/math].
- [math]1 + X[/math].
- [math]3X[/math].
- [math]aX + b[/math].