exercise:C2036c7349: 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 and define the '' standardized version'' <math>X^*</math> of <math>X</math> by: <math display="block"> X^* = \frac {X - \mu}\sigma\ . </math> <ul><li> Show that <math>P(|X^*| \geq a) \leq 1/a^2</...") |
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Let <math>X</math> be a continuous random variable and define the ''standardized version'' <math>X^*</math> of <math>X</math> by: | |||
standardized version'' <math>X^*</math> of <math>X</math> by: | |||
<math display="block"> | <math display="block"> | ||
X^* = \frac {X - \mu}\sigma\ . | X^* = \frac {X - \mu}\sigma\ . | ||
</math> | </math> | ||
<ul><li> Show that <math>P(|X^*| \geq a) \leq 1/a^2</math>. | <ul style="list-style-type:lower-alpha"><li> Show that <math>P(|X^*| \geq a) \leq 1/a^2</math>. | ||
</li> | </li> | ||
<li> If <math>X</math> is the random variable of | <li> If <math>X</math> is the random variable of [[exercise:63ec956b0e |Exercise]], find | ||
bounds for <math>P(|X^*| \geq 2)</math>, <math>P(|X^*| \geq 5)</math>, and <math>P(|X^*| \geq 9)</math>. | bounds for <math>P(|X^*| \geq 2)</math>, <math>P(|X^*| \geq 5)</math>, and <math>P(|X^*| \geq 9)</math>. | ||
</li> | </li> | ||
</ul> | </ul> | ||
Latest revision as of 23:49, 14 June 2024
Let [math]X[/math] be a continuous random variable and define the standardized version [math]X^*[/math] of [math]X[/math] by:
[[math]]
X^* = \frac {X - \mu}\sigma\ .
[[/math]]
- Show that [math]P(|X^*| \geq a) \leq 1/a^2[/math].
- If [math]X[/math] is the random variable of Exercise, find bounds for [math]P(|X^*| \geq 2)[/math], [math]P(|X^*| \geq 5)[/math], and [math]P(|X^*| \geq 9)[/math].