exercise:26ad10c5c7: 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>T</math> be a random variable with range <math>[0,\infty]</math> and <math>f_T</math> its density function. Find <math>\mu(T)</math> and <math>\sigma^2(T)</math> if, for <math>t < 0</math>, <math>f_T(t) = 0</math>, and for <math>t >...") |
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Let <math>T</math> be a random variable with range <math>[0,\infty]</math> and | |||
<math>f_T</math> its density function. Find <math>\mu(T)</math> and <math>\sigma^2(T)</math> if, for <math>t < 0</math>, <math>f_T(t) | <math>f_T</math> its density function. Find <math>\mu(T)</math> and <math>\sigma^2(T)</math> if, for <math>t < 0</math>, <math>f_T(t) | ||
= 0</math>, and for <math>t > 0</math>, | = 0</math>, and for <math>t > 0</math>, | ||
<ul><li> <math>f_T(t) = 3e^{-3t}</math>. | <ul style="list-style-type:lower-alpha"><li> <math>f_T(t) = 3e^{-3t}</math>. | ||
</li> | </li> | ||
<li> <math>f_T(t) = 9te^{-3t}</math>. | <li> <math>f_T(t) = 9te^{-3t}</math>. | ||
Latest revision as of 21:37, 14 June 2024
Let [math]T[/math] be a random variable with range [math][0,\infty][/math] and [math]f_T[/math] its density function. Find [math]\mu(T)[/math] and [math]\sigma^2(T)[/math] if, for [math]t \lt 0[/math], [math]f_T(t) = 0[/math], and for [math]t \gt 0[/math],
- [math]f_T(t) = 3e^{-3t}[/math].
- [math]f_T(t) = 9te^{-3t}[/math].
- [math]f_T(t) = 3/(1 + t)^4[/math].