exercise:Cb7313ebe2: 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> A surveyor is measuring the height of a cliff known to be about 1000 feet. He assumes his instrument is properly calibrated and that his measurement errors are independent, with mean <math>\mu = 0</math> and variance <math>\sigma^2 = 10</math>....") |
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A surveyor is measuring the height of a cliff known to be about 1000 feet. He assumes his instrument is properly calibrated and that his measurement | |||
feet. He assumes his instrument is properly calibrated and that his measurement | |||
errors are independent, with mean <math>\mu = 0</math> and variance <math>\sigma^2 = 10</math>. He | errors are independent, with mean <math>\mu = 0</math> and variance <math>\sigma^2 = 10</math>. He | ||
plans to take <math>n</math> measurements and form the average. Estimate, using | plans to take <math>n</math> measurements and form the average. Estimate, using | ||
Latest revision as of 23:26, 14 June 2024
A surveyor is measuring the height of a cliff known to be about 1000 feet. He assumes his instrument is properly calibrated and that his measurement errors are independent, with mean [math]\mu = 0[/math] and variance [math]\sigma^2 = 10[/math]. He plans to take [math]n[/math] measurements and form the average. Estimate, using (a) Chebyshev's inequality and (b) the normal approximation, how large [math]n[/math] should be if he wants to be 95 percent sure that his average falls within 1 foot of the true value. Now estimate, using (a) and (b), what value should [math]\sigma^2[/math] have if he wants to make only 10 measurements with the same confidence?