exercise:760b042e94: 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> A radioactive material emits <math>\alpha</math>-particles at a rate described by the density function <math display="block"> f(t) = .1e^{-.1t}\ . </math> Find the probability that a particle is emitted in the first 10 seconds, given that <ul><li...") |
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A radioactive material emits <math>\alpha</math>-particles at a rate described by the density function | |||
the density function | |||
<math display="block"> | <math display="block"> | ||
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Find the probability | Find the probability | ||
that a particle is emitted in the first 10 seconds, given that | that a particle is emitted in the first 10 seconds, given that | ||
<ul><li> no particle is emitted in the first second. | <ul style="list-style-type:lower-alpha"><li> no particle is emitted in the first second. | ||
</li> | </li> | ||
<li> no particle is emitted in the first 5 seconds. | <li> no particle is emitted in the first 5 seconds. | ||
Latest revision as of 00:25, 14 June 2024
A radioactive material emits [math]\alpha[/math]-particles at a rate described by the density function
[[math]]
f(t) = .1e^{-.1t}\ .
[[/math]]
Find the probability that a particle is emitted in the first 10 seconds, given that
- no particle is emitted in the first second.
- no particle is emitted in the first 5 seconds.
- a particle is emitted in the first 3 seconds.
- a particle is emitted in the first 20 seconds.