exercise:43b0a8aa95: Difference between revisions
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(Created page with "Choose a number <math>U</math> from the interval <math>[0,1]</math> with uniform distribution. Find the density for the random variables <math>Y = |U - 1/2|</math>. <ul class="mw-excansopts"> <li><math display ="block">f(y) = \begin{cases}2|y-1/2|, \, 0 \leq y \leq 1 \\ 0, \, \textrm{Otherwise} \end{cases}</math></li> <li><math display ="block">f(y) = \begin{cases}1/2, \, 0 \leq y \leq 2\\ 0, \, \textrm{Otherwise} \end{cases}</math></li> <li><math display ="block">f(y)...") |
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<li><math display ="block">f(y) = \begin{cases}2 - |y-1/2|, \, 0 \leq y \leq 1 \\ 0, \, \textrm{Otherwise} \end{cases}</math></li> | <li><math display ="block">f(y) = \begin{cases}2 - |y-1/2|, \, 0 \leq y \leq 1 \\ 0, \, \textrm{Otherwise} \end{cases}</math></li> | ||
<li><math display ="block">f(y) = \begin{cases}2, \, 0 \leq y \leq 1/2 \\ 0, \, \textrm{Otherwise} \end{cases}</math></li> | <li><math display ="block">f(y) = \begin{cases}2, \, 0 \leq y \leq 1/2 \\ 0, \, \textrm{Otherwise} \end{cases}</math></li> | ||
<li><math display ="block">\begin{cases}2y, \, 0 \leq y \leq 1 \\ 0, \, \textrm{Otherwise} \end{cases}</math></li> | <li><math display ="block">f(y) = \begin{cases}2y, \, 0 \leq y \leq 1 \\ 0, \, \textrm{Otherwise} \end{cases}</math></li> | ||
</ul> | </ul> | ||
Latest revision as of 22:43, 28 June 2024
Choose a number [math]U[/math] from the interval [math][0,1][/math] with uniform distribution. Find the density for the random variables [math]Y = |U - 1/2|[/math].
- [[math]]f(y) = \begin{cases}2|y-1/2|, \, 0 \leq y \leq 1 \\ 0, \, \textrm{Otherwise} \end{cases}[[/math]]
- [[math]]f(y) = \begin{cases}1/2, \, 0 \leq y \leq 2\\ 0, \, \textrm{Otherwise} \end{cases}[[/math]]
- [[math]]f(y) = \begin{cases}2 - |y-1/2|, \, 0 \leq y \leq 1 \\ 0, \, \textrm{Otherwise} \end{cases}[[/math]]
- [[math]]f(y) = \begin{cases}2, \, 0 \leq y \leq 1/2 \\ 0, \, \textrm{Otherwise} \end{cases}[[/math]]
- [[math]]f(y) = \begin{cases}2y, \, 0 \leq y \leq 1 \\ 0, \, \textrm{Otherwise} \end{cases}[[/math]]
References
Doyle, Peter G. (2006). "Grinstead and Snell's Introduction to Probability" (PDF). Retrieved June 6, 2024.