exercise:1126205870: 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 Acme Super light bulb is known to have a useful life described by the density function <math display="block"> f(t) = .01e^{-.01t}\ , </math> where time <math>t</math> is measured in hours. <ul><li> Find the ''failure rate'' of this bulb (...") |
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The Acme Super light bulb is known to have a useful life described by the density function | |||
described by the density function | |||
<math display="block"> | <math display="block"> | ||
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</math> | </math> | ||
where time <math>t</math> is measured in hours. | where time <math>t</math> is measured in hours. | ||
<ul><li> Find the ''failure rate'' of this bulb | |||
(see | <ul style="list-style-type:lower-alpha"><li> Find the ''failure rate'' of this bulb (see [[exercise:B8ae29be7e|exercise]]). | ||
</li> | </li> | ||
<li> Find the ''reliability'' of this bulb after 20 hours. | <li> Find the ''reliability'' of this bulb after 20 hours. | ||
Latest revision as of 23:32, 13 June 2024
The Acme Super light bulb is known to have a useful life described by the density function
[[math]]
f(t) = .01e^{-.01t}\ ,
[[/math]]
where time [math]t[/math] is measured in hours.
- Find the failure rate of this bulb (see exercise).
- Find the reliability of this bulb after 20 hours.
- Given that it lasts 20 hours, find the probability that the bulb lasts another 20 hours.
- Find the probability that the bulb burns out in the forty-first hour, given that it lasts 40 hours.