exercise:B8ae29be7e: Difference between revisions
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\newcommand{\mathds}{\mathbb}</math></div> Assume that a new light bulb will burn out after <math>t</math> | \newcommand{\mathds}{\mathbb}</math></div> Assume that a new light bulb will burn out after <math>t</math> hours, where <math>t</math> is chosen from <math>[0,\infty)</math> with an exponential density | ||
hours, where <math>t</math> is chosen from <math>[0,\infty)</math> with an exponential density | |||
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Latest revision as of 22:37, 12 June 2024
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Assume that a new light bulb will burn out after [math]t[/math] hours, where [math]t[/math] is chosen from [math][0,\infty)[/math] with an exponential density
[[math]]
f(t) = \lambda e^{-\lambda t}\ .
[[/math]]
In this context, [math]\lambda[/math] is often called the failure rate of the bulb.
- Assume that [math]\lambda = 0.01[/math], and find the probability that the bulb will not burn out before [math]T[/math] hours. This probability is often called the reliability of the bulb.
- For what [math]T[/math] is the reliability of the bulb [math] = 1/2[/math]?