exercise:F39cb86b1c: 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 number <math>U</math> is chosen at random in the interval <math>[0,1]</math>. Find the probability that <ul><li> <math>R = U^2 < 1/4</math>. </li> <li> <math>S = U(1 - U) < 1/4</math>. </li> <li> <math>T = U/(1 - U) < 1/4</math>. </li> </ul>") |
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A number <math>U</math> is chosen at random in the interval | |||
<math>[0,1]</math>. Find the probability that | <math>[0,1]</math>. Find the probability that | ||
<ul><li> <math>R = U^2 < 1/4</math>. | <ul style="list-style-type:lower-alpha"><li> <math>R = U^2 < 1/4</math>. | ||
</li> | </li> | ||
<li> <math>S = U(1 - U) < 1/4</math>. | <li> <math>S = U(1 - U) < 1/4</math>. | ||
Latest revision as of 01:03, 14 June 2024
A number [math]U[/math] is chosen at random in the interval [math][0,1][/math]. Find the probability that
- [math]R = U^2 \lt 1/4[/math].
- [math]S = U(1 - U) \lt 1/4[/math].
- [math]T = U/(1 - U) \lt 1/4[/math].