exercise:Bc4453a0ca: 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> Suppose one hundred numbers <math>X_1</math>, <math>X_2</math>, \dots, <math>X_{100}</math> are chosen independently at random from <math>[0,20]</math>. Let <math>S = X_1 + X_2 +\cdots+ X_{100}</math> be the sum, <math>A = S/100</math> the averag...") |
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Suppose one hundred numbers <math>X_1</math>, <math>X_2</math>, \dots, <math>X_{100}</math> are chosen independently at random from <math>[0,20]</math>. Let <math>S = X_1 + X_2 +\cdots+ X_{100}</math> | |||
independently at random from <math>[0,20]</math>. Let <math>S = X_1 + X_2 +\cdots+ X_{100}</math> | |||
be the sum, <math>A = S/100</math> the average, and <math>S^* = (S - 1000)/(10/\sqrt3)</math> the | be the sum, <math>A = S/100</math> the average, and <math>S^* = (S - 1000)/(10/\sqrt3)</math> the | ||
standardized sum. Find lower bounds for the probabilities | standardized sum. Find lower bounds for the probabilities | ||
<ul><li> <math>P(|S - 1000| \leq 100)</math>. | <ul style="list-style-type:lower-alpha"><li> <math>P(|S - 1000| \leq 100)</math>. | ||
</li> | </li> | ||
<li> <math>P(|A - 10| \leq 1)</math>. | <li> <math>P(|A - 10| \leq 1)</math>. | ||
Latest revision as of 23:50, 14 June 2024
Suppose one hundred numbers [math]X_1[/math], [math]X_2[/math], \dots, [math]X_{100}[/math] are chosen independently at random from [math][0,20][/math]. Let [math]S = X_1 + X_2 +\cdots+ X_{100}[/math] be the sum, [math]A = S/100[/math] the average, and [math]S^* = (S - 1000)/(10/\sqrt3)[/math] the standardized sum. Find lower bounds for the probabilities
- [math]P(|S - 1000| \leq 100)[/math].
- [math]P(|A - 10| \leq 1)[/math].
- [math]P(|S^*| \leq \sqrt3)[/math].