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 with values normally distributed over <math>(-\infty,+\infty)</math> with mean <math>\mu = 0</math> and variance <math>\sigma^2 = 1</math>. <ul><li> Using Chebyshev's Inequality, find upper bounds...")
BBy Bot
Jun 09'24
Exercise
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Let [math]X[/math] be a continuous random variable with values normally
distributed over [math](-\infty,+\infty)[/math] with mean [math]\mu = 0[/math] and variance [math]\sigma^2 = 1[/math].
- Using Chebyshev's Inequality, find upper bounds for the following probabilities: [math]P(|X| \geq 1)[/math], [math]P(|X| \geq 2)[/math], and [math]P(|X| \geq 3)[/math].
- The area under the normal curve between [math]-1[/math] and 1 is .6827, between [math]-2[/math] and 2 is .9545, and between [math]-3[/math] and 3 it is .9973 (see the table in Appendix A). Compare your bounds in (a) with these exact values. How good is Chebyshev's Inequality in this case?