exercise:3dbebbe250: 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 <math>f_X</math> its density function. Find <math>\mu(X)</math> and <math>\sigma^2(X)</math> if, for <math>|x| > 1</math>, <math>f_X(x) = 0</math>, and for <math>|x| <...") |
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Let <math>X</math> be a random variable with range <math>[-1,1]</math> and | |||
<math>f_X</math> its density function. Find <math>\mu(X)</math> and <math>\sigma^2(X)</math> if, for <math>|x| > 1</math>, | <math>f_X</math> its density function. Find <math>\mu(X)</math> and <math>\sigma^2(X)</math> if, for <math>|x| > 1</math>, | ||
<math>f_X(x) = 0</math>, and for <math>|x| < 1</math>, | <math>f_X(x) = 0</math>, and for <math>|x| < 1</math>, | ||
<ul><li> <math>f_X(x) = (3/4)(1 - x^2)</math>. | <ul style="list-style-type:lower-alpha"><li> <math>f_X(x) = (3/4)(1 - x^2)</math>. | ||
</li> | </li> | ||
<li> <math>f_X(x) = (\pi/4)\cos(\pi x/2)</math>. | <li> <math>f_X(x) = (\pi/4)\cos(\pi x/2)</math>. | ||
Latest revision as of 22:36, 14 June 2024
Let [math]X[/math] be a random variable with range [math][-1,1][/math] and [math]f_X[/math] its density function. Find [math]\mu(X)[/math] and [math]\sigma^2(X)[/math] if, for [math]|x| \gt 1[/math], [math]f_X(x) = 0[/math], and for [math]|x| \lt 1[/math],
- [math]f_X(x) = (3/4)(1 - x^2)[/math].
- [math]f_X(x) = (\pi/4)\cos(\pi x/2)[/math].
- [math]f_X(x) = (x + 1)/2[/math].
- [math]f_X(x) = (3/8)(x + 1)^2[/math].