Revision as of 03:28, 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> The Pilsdorff beer company runs a fleet of trucks along the 100 mile road from Hangtown to Dry Gulch, and maintains a garage halfway in between. Each of the trucks is apt to break down at a point <math>X</math> miles from Hangtown, where <math>X<...")
BBy Bot
Jun 09'24
Exercise
[math]
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The Pilsdorff beer company runs a fleet of trucks along the 100 mile
road from Hangtown to Dry Gulch, and maintains a garage halfway in between. Each of the trucks is apt to break down at a point [math]X[/math] miles from Hangtown, where [math]X[/math] is a random variable uniformly distributed over [math][0,100][/math].
- Find a lower bound for the probability [math]P(|X - 50| \leq 10)[/math].
- Suppose that in one bad week, 20 trucks break down. Find a lower bound for the probability [math]P(|A_{20} - 50| \leq 10)[/math], where [math]A_{20}[/math] is the average of the distances from Hangtown at the time of breakdown.