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Distribuciones discretas - Historial de revisiones
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83.56.129.131: /* Definición */
2007-01-12T22:38:36Z
<p><span class="autocomment">Definición</span></p>
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<td colspan='2' style="background-color: white; color:black;">← Revisión anterior</td>
<td colspan='2' style="background-color: white; color:black;">Revisión de 22:38 12 ene 2007</td>
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<tr><td colspan="2" class="diff-lineno">Línea 438:</td>
<td colspan="2" class="diff-lineno">Línea 438:</td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;"> </del><math></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\mathrm{P}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\mathrm{P}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\left(</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\left(</div></td></tr>
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83.56.129.131
http://wikillerato.org/index.php?title=Distribuciones_discretas&diff=2685&oldid=prev
Fjmolina en 22:46 27 dic 2006
2006-12-27T22:46:16Z
<p></p>
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<td colspan='2' style="background-color: white; color:black;">← Revisión anterior</td>
<td colspan='2' style="background-color: white; color:black;">Revisión de 22:46 27 dic 2006</td>
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<tr><td colspan="2" class="diff-lineno">Línea 533:</td>
<td colspan="2" class="diff-lineno">Línea 533:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>&nbsp; "pruebas". Cada una de estas pruebas</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>&nbsp; "pruebas". Cada una de estas pruebas</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>es el nacimiento de un hijo. <del style="color: red; font-weight: bold; text-decoration: none;">Supongomos </del>que la probabilidad de que un hijo sea chico es</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>es el nacimiento de un hijo. <ins style="color: red; font-weight: bold; text-decoration: none;">Supongamos </ins>que la probabilidad de que un hijo sea chico es</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>de &nbsp;</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>de &nbsp;</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>p \, = \, 5</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>p \, = \<ins style="color: red; font-weight: bold; text-decoration: none;">, 0</ins>,5</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>. Entonces, si &nbsp;</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>. Entonces, si &nbsp;</div></td></tr>
<tr><td colspan="2" class="diff-lineno">Línea 542:</td>
<td colspan="2" class="diff-lineno">Línea 542:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>X</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>X</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&nbsp; es el numero de hijos varones, <del style="color: red; font-weight: bold; text-decoration: none;">entonces</del>:</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&nbsp; es el numero de hijos varones, <ins style="color: red; font-weight: bold; text-decoration: none;">se tiene que</ins>:</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><br/></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><br/></div></td></tr>
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Fjmolina
http://wikillerato.org/index.php?title=Distribuciones_discretas&diff=2683&oldid=prev
Fjmolina en 22:44 27 dic 2006
2006-12-27T22:44:49Z
<p></p>
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<td colspan='2' style="background-color: white; color:black;">← Revisión anterior</td>
<td colspan='2' style="background-color: white; color:black;">Revisión de 22:44 27 dic 2006</td>
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<tr><td colspan="2" class="diff-lineno">Línea 267:</td>
<td colspan="2" class="diff-lineno">Línea 267:</td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>==Definición==</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">=</ins>==Definición<ins style="color: red; font-weight: bold; text-decoration: none;">=</ins>==</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><br/></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><br/></div></td></tr>
<tr><td colspan="2" class="diff-lineno">Línea 556:</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> { 5 \atop 3 }</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> { 5 \atop 3 }</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\right)</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\right)</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>\cdot 0,5^<del style="color: red; font-weight: bold; text-decoration: none;">r </del>\cdot</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>\cdot 0,5^<ins style="color: red; font-weight: bold; text-decoration: none;">3 </ins>\cdot</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\left(</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\left(</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> \, 1 \, - \, 0,5 \,</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> \, 1 \, - \, 0,5 \,</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\right)</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\right)</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>^</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>^</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>\left(</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">{</ins></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;"> </del>\, 5 \, - \, 3 \,</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"> </ins>\left(</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>\right)</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"> </ins>\, 5 \, - \, 3 \,</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"> </ins>\right)</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">}</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\, = \, \frac{5!}{3!2!} \cdot 0,5^5 \, = \, 10 \cdot 0,5^5</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\, = \, \frac{5!}{3!2!} \cdot 0,5^5 \, = \, 10 \cdot 0,5^5</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td></tr>
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Fjmolina
http://wikillerato.org/index.php?title=Distribuciones_discretas&diff=2682&oldid=prev
Fjmolina en 22:43 27 dic 2006
2006-12-27T22:43:09Z
<p></p>
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<td colspan='2' style="background-color: white; color:black;">Revisión de 22:43 27 dic 2006</td>
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<tr><td colspan="2" class="diff-lineno">Línea 264:</td>
<td colspan="2" class="diff-lineno">Línea 264:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Distribución binomial==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Distribución binomial==</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><br/></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">==Definición==</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><br/></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><br/></div></td></tr>
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Fjmolina
http://wikillerato.org/index.php?title=Distribuciones_discretas&diff=2681&oldid=prev
Fjmolina en 22:42 27 dic 2006
2006-12-27T22:42:11Z
<p></p>
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<td colspan='2' style="background-color: white; color:black;">Revisión de 22:42 27 dic 2006</td>
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<tr><td colspan="2" class="diff-lineno">Línea 463:</td>
<td colspan="2" class="diff-lineno">Línea 463:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\left(</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\left(</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div> <del style="color: red; font-weight: bold; text-decoration: none;">\, </del>{ n \atop r }</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> { n \atop r }</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\right)</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\right)</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\, = \, \frac{n!}{r!\left( \, n \, - \, r \, \right)!}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\, = \, \frac{n!}{r!\left( \, n \, - \, r \, \right)!}</div></td></tr>
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<td colspan="2" class="diff-lineno">Línea 513:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>n! \, = \, n \cdot \left( \,n \, - \, 1 \, \right) \cdot \ldots 2 \cdot 1</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>n! \, = \, n \cdot \left( \,n \, - \, 1 \, \right) \cdot \ldots 2 \cdot 1</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><br/></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">===Ejemplo===</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><br/></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">¿Cual es la probabilidad de que en una familia con 5 hijos, 3 sean chicos y 2 chicas?</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><br/></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">En este caso el experimento aleatorio consiste de &nbsp;</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">n \, = \, 5</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">&nbsp; "pruebas". Cada una de estas pruebas</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">es el nacimiento de un hijo. Supongomos que la probabilidad de que un hijo sea chico es</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">de &nbsp;</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">p \, = \, 5</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">. Entonces, si &nbsp;</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">X</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">&nbsp; es el numero de hijos varones, entonces:</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><br/></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><center></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">\mathrm{P}</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">\left(</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"> \, X \, = \, 3 \,</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">\right)</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">\, = \,</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">\left(</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"> { 5 \atop 3 }</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">\right)</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">\cdot 0,5^r \cdot</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">\left(</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"> \, 1 \, - \, 0,5 \,</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">\right)</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">^</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">\left(</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"> \, 5 \, - \, 3 \,</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">\right)</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">\, = \, \frac{5!}{3!2!} \cdot 0,5^5 \, = \, 10 \cdot 0,5^5</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></center></ins></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Category:Matemáticas]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Category:Matemáticas]]</div></td></tr>
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Fjmolina
http://wikillerato.org/index.php?title=Distribuciones_discretas&diff=2680&oldid=prev
Fjmolina en 22:33 27 dic 2006
2006-12-27T22:33:26Z
<p></p>
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<td colspan='2' style="background-color: white; color:black;">← Revisión anterior</td>
<td colspan='2' style="background-color: white; color:black;">Revisión de 22:33 27 dic 2006</td>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>Se llama '''''función de probabilidad de una variable aleatoria discreta &nbsp; <math>X</math></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Se llama '''''función de probabilidad de una variable aleatoria discreta<ins style="color: red; font-weight: bold; text-decoration: none;">''''' </ins>&nbsp;</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">''''' </del>a la aplicacion que a cada valor de &nbsp;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><math></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>X</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></math></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">&nbsp; </ins>a la aplicacion que a cada valor de &nbsp;</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>x_i</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>x_i</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>La función de distribución de cualquier variable aleatoria discreta tiene las <del style="color: red; font-weight: bold; text-decoration: none;">siguentes</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>La función de distribución de cualquier variable aleatoria discreta tiene las <ins style="color: red; font-weight: bold; text-decoration: none;">siguientes</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>caracteristicas:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>caracteristicas:</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>x</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>x</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&nbsp; menor que el menor valor de la variable aleatoria, y es igual a <del style="color: red; font-weight: bold; text-decoration: none;">la unidad </del>para</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&nbsp; menor que el menor valor de la variable aleatoria, y es igual a <ins style="color: red; font-weight: bold; text-decoration: none;">uno </ins>para</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>todo valor de &nbsp;</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>todo valor de &nbsp;</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>i \, = \, 1, \, \ldots, \, n \, - \, 1</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>i \, = \, 1, \, \ldots, \, n \, - \, 1</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">&nbsp; </del></div></td><td colspan="2"> </td></tr>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>1. En cada prueba del experimento sólo son posibles dos resultados: el suceso &nbsp; <math> A </math> , llamado ''exito'', y su contrario, &nbsp; <math> \bar{A} </math>, llamado ''fracaso''.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"> </ins>1. En cada prueba del experimento sólo son posibles dos resultados: el suceso &nbsp; <math> A </math> , llamado</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"> </ins>''exito'', y su contrario, &nbsp; <math> \bar{A} </math>, llamado ''fracaso''.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>2. El resultado de cada prueba es independiente de los resultados obtenidos anteriormente.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"> </ins>2. El resultado de cada prueba es independiente de los resultados obtenidos anteriormente.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>3. La probabilidad de &nbsp; <math> A </math> , que denotamos por &nbsp; <math> p </math> , no varía de una prueba a otra.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"> </ins>3. La probabilidad de &nbsp; <math> A </math> , que denotamos por &nbsp; <math> p</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"> </ins></math> , no varía de una prueba a otra.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>4. En cada experimento se realizan &nbsp; <math> n </math> &nbsp; pruebas idénticas.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"> </ins>4. En cada experimento se realizan &nbsp; <math> n </math> &nbsp; pruebas idénticas.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> \, X \, = \, 2 \,</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> \, X \, = \, 2 \,</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\right\}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\right\}</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div></math></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></math>:</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><math></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"> </ins><math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\mathrm{P}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\mathrm{P}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\left(</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\left(</div></td></tr>
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Fjmolina
http://wikillerato.org/index.php?title=Distribuciones_discretas&diff=2671&oldid=prev
213.97.196.225: /* Función de probabilidad */
2006-12-27T09:53:17Z
<p><span class="autocomment">Función de probabilidad</span></p>
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<td colspan='2' style="background-color: white; color:black;">← Revisión anterior</td>
<td colspan='2' style="background-color: white; color:black;">Revisión de 09:53 27 dic 2006</td>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>Se llama '''''función de probabilidad de una variable aleatoria discreta &nbsp;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Se llama '''''función de probabilidad de una variable aleatoria discreta &nbsp; <math>X</math></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><math></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>X</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div></math></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>''''' a la aplicacion que a cada valor de &nbsp;</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>''''' a la aplicacion que a cada valor de &nbsp;</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td></tr>
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213.97.196.225
http://wikillerato.org/index.php?title=Distribuciones_discretas&diff=2670&oldid=prev
213.97.196.225: /* Distribución binomial */
2006-12-27T09:51:48Z
<p><span class="autocomment">Distribución binomial</span></p>
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<td colspan='2' style="background-color: white; color:black;">Revisión de 09:51 27 dic 2006</td>
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<td colspan="2" class="diff-lineno">Línea 434:</td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;"> </del><math></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\mathrm{P}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\mathrm{P}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\left(</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\left(</div></td></tr>
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213.97.196.225
http://wikillerato.org/index.php?title=Distribuciones_discretas&diff=2669&oldid=prev
213.97.196.225: /* Distribución binomial */
2006-12-27T09:51:02Z
<p><span class="autocomment">Distribución binomial</span></p>
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<td colspan='2' style="background-color: white; color:black;">← Revisión anterior</td>
<td colspan='2' style="background-color: white; color:black;">Revisión de 09:51 27 dic 2006</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;"> </del>1. En cada prueba del experimento sólo son posibles dos resultados: el suceso &nbsp; <math> A </math> , llamado</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>1. En cada prueba del experimento sólo son posibles dos resultados: el suceso &nbsp; <math> A </math> , llamado ''exito'', y su contrario, &nbsp; <math> \bar{A} </math>, llamado ''fracaso''.</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;"> </del>''exito'', y su contrario, &nbsp; <math> \bar{A} </math>, llamado ''fracaso''.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;"> </del>2. El resultado de cada prueba es independiente de los resultados obtenidos anteriormente.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>2. El resultado de cada prueba es independiente de los resultados obtenidos anteriormente.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;"> </del>3. La probabilidad de &nbsp; <math> A </math> , que denotamos por &nbsp; <math> p</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>3. La probabilidad de &nbsp; <math> A </math> , que denotamos por &nbsp; <math> p </math> , no varía de una prueba a otra.</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;"> </del></math> , no varía de una prueba a otra.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;"> </del>4. En cada experimento se realizan &nbsp; <math> n </math> &nbsp; pruebas idénticas.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>4. En cada experimento se realizan &nbsp; <math> n </math> &nbsp; pruebas idénticas.</div></td></tr>
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213.97.196.225
http://wikillerato.org/index.php?title=Distribuciones_discretas&diff=2666&oldid=prev
Fjmolina en 02:07 27 dic 2006
2006-12-27T02:07:20Z
<p></p>
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<td colspan='2' style="background-color: white; color:black;">Revisión de 02:07 27 dic 2006</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>. ( Aqui el exito es que salga cara ). Existen tres posibilidades de que ocurra &nbsp;</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>. ( Aqui el exito es que salga cara ). Existen tres posibilidades de que ocurra &nbsp;</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>X \, = \, 2</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">\left\{</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"> \, </ins>X \, = \, 2 <ins style="color: red; font-weight: bold; text-decoration: none;">\,</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">\right\}</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:</div></td></tr>
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Fjmolina