exercise:3f24aed445: 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 random variable with range <math>[-1,1]</math> and let <math>f_X(x)</math> be the density function of <math>X</math>. Find <math>\mu(X)</math> and <math>\sigma^2(X)</math> if, for <math>|x| < 1</math>, <ul><li> <math>f_X(...") |
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Let <math>X</math> be a random variable with range <math>[-1,1]</math> and let <math>f_X(x)</math> be the density function of <math>X</math>. Find <math>\mu(X)</math> and <math>\sigma^2(X)</math> if, for <math>|x| | |||
<math>f_X(x)</math> be the density function of <math>X</math>. Find <math>\mu(X)</math> and <math>\sigma^2(X)</math> if, for <math>|x| | |||
< 1</math>, | < 1</math>, | ||
<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) = |x|</math>. | <li> <math>f_X(x) = |x|</math>. | ||
Latest revision as of 21:36, 14 June 2024
Let [math]X[/math] be a random variable with range [math][-1,1][/math] and let [math]f_X(x)[/math] be the density function of [math]X[/math]. Find [math]\mu(X)[/math] and [math]\sigma^2(X)[/math] if, for [math]|x| \lt 1[/math],
- [math]f_X(x) = 1/2[/math].
- [math]f_X(x) = |x|[/math].
- [math]f_X(x) = 1 - |x|[/math].
- [math]f_X(x) = (3/2) x^2[/math].