exercise:77ea6286d5: 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 cumulative distribution function <math>F</math>. The ''median'' of <math>X</math> is the value <math>m</math> for which <math>F(m) = 1/2</math>. Then <math>X < m</math> with probability 1/2 and <ma...") |
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Let <math>X</math> be a random variable with cumulative distribution function | |||
<math>F</math>. The ''median'' of <math>X</math> is the value <math>m</math> for which <math>F(m) = 1/2</math>. Then | <math>F</math>. The ''median'' of <math>X</math> is the value <math>m</math> for which <math>F(m) = 1/2</math>. Then | ||
<math>X < m</math> with probability 1/2 and <math>X > m</math> with probability 1/2. Find <math>m</math> if <math>X</math> is | <math>X < m</math> with probability 1/2 and <math>X > m</math> with probability 1/2. Find <math>m</math> if <math>X</math> is | ||
<ul><li> uniformly distributed over the interval <math>[a,b]</math>. | <ul style="list-style-type:lower-alpha"><li> uniformly distributed over the interval <math>[a,b]</math>. | ||
</li> | </li> | ||
<li> normally distributed with parameters <math>\mu</math> and <math>\sigma</math>. | <li> normally distributed with parameters <math>\mu</math> and <math>\sigma</math>. | ||
Latest revision as of 02:06, 14 June 2024
Let [math]X[/math] be a random variable with cumulative distribution function [math]F[/math]. The median of [math]X[/math] is the value [math]m[/math] for which [math]F(m) = 1/2[/math]. Then [math]X \lt m[/math] with probability 1/2 and [math]X \gt m[/math] with probability 1/2. Find [math]m[/math] if [math]X[/math] is
- uniformly distributed over the interval [math][a,b][/math].
- normally distributed with parameters [math]\mu[/math] and [math]\sigma[/math].
- exponentially distributed with parameter [math]\lambda[/math].