exercise:7efe91a34d: 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> 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<...") |
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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. | |||
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, | 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>. | where <math>X</math> is a random variable uniformly distributed over <math>[0,100]</math>. | ||
<ul><li> Find a lower bound for the probability <math>P(|X - 50| \leq 10)</math>. | <ul style="list-style-type:lower-alpha"><li> Find a lower bound for the probability <math>P(|X - 50| \leq 10)</math>. | ||
</li> | </li> | ||
<li> Suppose that in one bad week, 20 trucks break down. Find a lower bound | <li> Suppose that in one bad week, 20 trucks break down. Find a lower bound | ||
Latest revision as of 23:50, 14 June 2024
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.