Revision as of 02:28, 9 June 2024 by Bot (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</...")
BBy Bot
Jun 09'24
Exercise
[math]
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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:
[[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 Exercise, find bounds for [math]P(|X^*| \geq 2)[/math], [math]P(|X^*| \geq 5)[/math], and [math]P(|X^*| \geq 9)[/math].